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Class 8 Exam > Class 8 Notes > RD Sharma Solutions for Class 8 Mathematics > RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics PDF Download

Q: 1. What is the formula to find the volume of a cube?

Ans. The formula to find the volume of a cube is V = s^3, where V is the volume and s is the length of one side of the cube.

Q: 2. How can I calculate the cube root of a number without a calculator?

Ans. To calculate the cube root of a number without a calculator, you can use the prime factorization method. Write the number as a product of prime factors, then group the factors into triples and calculate the product of the group. The product will be the cube root of the number.

Q: 3. What is the difference between a perfect cube and a cube number?

Ans. A perfect cube is a number that can be expressed as the cube of an integer, while a cube number is any number raised to the power of 3. In other words, all perfect cubes are cube numbers, but not all cube numbers are perfect cubes.

Q: 4. How can I find the cube root of a decimal number?

Ans. To find the cube root of a decimal number, you can estimate the cube root by finding the closest whole number and then refine the estimate using the long division method. Divide the decimal number by the cube of the estimated whole number, and repeat the process until you reach the desired level of accuracy.

Q: 5. Can a cube have a negative volume?

Ans. No, a cube cannot have a negative volume. Volume is a measure of the amount of space occupied by an object, and it is always a positive value. Therefore, the volume of a cube is always positive, regardless of the sign of its side length.

Question 1: Making use of the cube root table, find the cube roots 7

Answer 1: Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics 1.913

Thus, the answer is 1.913.

**Question 2: Making use of the cube root table, find the cube root 70**

Answer 2: Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics 4.121

**Question 3: Making use of the cube root table, find the cube root 700**

Answer 3: We have:

$700 = 70 \times 10$
$∴$ Cube root of 700 will be in the column of against 70.

By the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics =8.879

Thus, the answer is 8.879.

**Question 4: Making use of the cube root table, find the cube root 7000**

Answer 4: We have:

$7000 = 70 \times 100$

By the cube root table, we have:

=1.913×10=19.13

**Question 5: Making use of the cube root table, find the cube root 1100**

Answer 5: We have:

$1100 = 11 \times 100$

By the cube root table, we have:

$\sqrt[3]{1100} = \sqrt[3]{11} \times \sqrt[3]{100} = 2.224 \times 4.642 = 10.323 (Up to three decimal places)$

Thus, the answer is 10.323.

**Question 6: Making use of the cube root table, find the cube root 780**

Answer 6: We have:

$780 = 78 \times 10$

$∴$ Cube root of 780 would be in the column of against 78.

By the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics = 9.205

Thus, the answer is 9.205.

**Question 7: Making use of the cube root table, find the cube root 7800**

Answer 7: We have:

$7800 = 78 \times 100$

By the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics =4.273×4.642=19.835 (upto three decimal places)

Thus, the answer is 19.835

Question 8: Making use of the cube root table, find the cube root 1346

Answer 8: By prime factorisation, we have:

1346=2×673⇒

Also

670<673<680⇒

From the cube root table, we have:

For the difference (680 $-$ 670), i.e., 10, the difference in the values

$= 8.794 - 8.750 = 0.044$

$∴$ For the difference of (673 $-$ 670), i.e., 3, the difference in the values

$= \frac{0.044}{10} \times 3 = 0.0132 = 0.013$ (upto three decimal places)

$\sqrt[3]{673} = 8.750 + 0.013 = 8.763$

Now

$\sqrt[3]{1346} = \sqrt[3]{2} \times \sqrt[3]{673} = 1.260 \times 8.763 = 11.041$ (upto three decimal places)

Thus, the answer is 11.041.

**Question 9: Making use of the cube root table, find the cube root 250**

Answer 9: We have:

$250 = 25 \times 100$

$∴$ Cube root of 250 would be in the column of against 25.

By the cube root table, we have:

Thus, the required cube root is 6.3.

**Question 10: Making use of the cube root table, find the cube root 5112**

Answer 10: By prime factorisation, we have:

5112=23×32×71⇒

By the cube root table, we have:

$\sqrt[3]{5112} = 2 \times \sqrt[3]{9} \times \sqrt[3]{71} = 2 \times 2.080 \times 4.141 = 17.227$ (upto three decimal places)

Thus, the required cube root is 17.227.

Question 11: Making use of the cube root table, find the cube root
9800

Answer 11: We have:

$9800 = 98 \times 100$
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

By cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{9800} = \sqrt[3]{98} \times \sqrt[3]{100} = 4.610 \times 4.642 = 21.40$ (upto three decimal places)

Thus, the required cube root is 21.40.

**Question 12: Making use of the cube root table, find the cube root 732**

Answer 12: We have:

730<732<740⇒

From cube root table, we have:

For the difference (740 $-$ 730), i.e., 10, the difference in values

$= 9.045 - 9.004 = 0.041$

$∴$ For the difference of (732 $-$ 730), i.e., 2, the difference in values

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics 2=0.0082

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics =9.004+0.008=9.012

**Question 13: Making use of the cube root table, find the cube root 7342**

Answer 13: We have:

7300<7342<7400⇒

From the cube root table, we have:

For the difference (7400 $-$ 7300), i.e., 100, the difference in values

=19.48−19.39=0.09

$∴$ For the difference of (7342 $-$ 7300), i.e., 42, the difference in the values

×42=0.0378=0.037

=19.39+0.037=19.427

**Question 14: Making use of the cube root table, find the cube root 133100**

Answer 14: We have:

133100=1331×100⇒

By cube root table, we have:

$\sqrt[3]{100} = 4.642$

=11×4.642=51.062

**Question 15: Making use of the cube root table, find the cube root 37800**

Answer 15: We have:

37800=23×33×175⇒

Also

170<175<180⇒

From cube root table, we have:

For the difference (180 $-$ 170), i.e., 10, the difference in values

$= 5.646 - 5.540 = 0.106$

$∴$ For the difference of (175 $-$ 170), i.e., 5, the difference in values

$= \frac{0.106}{10} \times 5 = 0.053$

$\sqrt[3]{175} = 5.540 + 0.053 = 5.593$

Now

37800=6× $37800 = 6 \times \sqrt[3]{175} = 6 \times 5.593 = 33.558$

Thus, the required cube root is 33.558.

**Question 16: Making use of the cube root table, find the cube root 0.27**

Answer 16: The number 0.27 can be written as 27/100.

Now

By cube root table, we have:

$\sqrt[3]{0.27} = \frac{3}{\sqrt[3]{100}} = \frac{3}{4.642} = 0.646$ .

Thus, the required cube root is 0.646.

**Question 17: Making use of the cube root table, find the cube root 8.6**

Answer 17: The number 8.6 can be written as 86/10.

Now

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

By cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{8.6} = \frac{\sqrt[3]{86}}{\sqrt[3]{10}} = \frac{4.414}{2.154} = 2.049$

Thus, the required cube root is 2.049.

**Question 18: Making use of the cube root table, find the cube root 0.86**

Answer 18: The number 0.86 could be written as 86/100.

Now

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

By cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{0.86} = \frac{\sqrt[3]{86}}{\sqrt[3]{100}} = \frac{4.414}{4.642} = 0.951$ (upto three decimal places)

Thus, the required cube root is 0.951.

**Question 19: Making use of the cube root table, find the cube root 8.65**

Answer 19: The number 8.65 could be written as 865/100.

Now

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

Also

860<865<870⇒ RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

From the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

For the difference (870 $-$ 860), i.e., 10, the difference in values

$= 9.546 - 9.510 = 0.036$
$∴$ For the difference of (865 $-$ 860), i.e., 5, the difference in values
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics ×5=0.018 (upto three decimal places)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{865} = 9.510 + 0.018 = 9.528$ (upto three decimal places)

From the cube root table, we also have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{8.65} = \frac{\sqrt[3]{865}}{\sqrt[3]{100}} = \frac{9.528}{4.642} = 2.053$ (upto three decimal places)

Thus, the required cube root is 2.053.

**Question 20: Making use of the cube root table, find the cube root 7532**

Answer 20: We have:

7500<7532<7600⇒

From the cube root table, we have:

For the difference (7600 $-$ 7500), i.e., 100, the difference in values

$= 19.66 - 19.57 = 0.09$

$∴$ For the difference of (7532 $-$ 7500), i.e., 32, the difference in values

$= \frac{0.09}{100} \times 32 = 0.0288 = 0.029$ (up to three decimal places)

=19.57+0.029=19.59975323=19.57+0.029=19.599

Question 21: Making use of the cube root table, find the cube root
833

Answer 21: We have:

830<833<840⇒

From the cube root table, we have:

For the difference (840 $-$ 830), i.e., 10, the difference in values

$= 9.435 - 9.398 = 0.037$

$∴$ For the difference (833 $-$ 830), i.e., 3, the difference in values

$= \frac{0.037}{10} \times 3 = 0.0111 = 0.011$ (upto three decimal places)

=9.398+0.011=9.4098333=9.398+0.011=9.409

**Question 22: Making use of the cube root table, find the cube root 34.2**

Answer 22: The number 34.2 could be written as 342/10.

Now

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

Also

340<342<350⇒ RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

From the cube root table, we have:
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

For the difference (350 $-$ 340), i.e., 10, the difference in values

$= 7.047 - 6.980 = 0.067$ .

$∴$ For the difference (342 $-$ 340), i.e., 2, the difference in values

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $= \frac{0.067}{10} \times 2 = 0.013$ (upto three decimal places)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{342} = 6.980 + 0.0134 = 6.993$ (upto three decimal places)

From the cube root table, we also have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics 3.246

Thus, the required cube root is 3.246.

Question 23: What is the length of the side of a cube whose volume is 275 cm³. Make use of the table for the cube root.

Answer 23: Volume of a cube is given by:

$V = a^{3}$ , where a = side of the cube

∴∴ Side of a cube = a= RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

If the volume of a cube is 275 cm³, the side of the cube will be RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

We have:

270<275<280⇒
RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

From the cube root table, we have:

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

For the difference (280 $-$ 270), i.e., 10, the difference in values

$= 6.542 - 6.463 = 0.079$

$∴$ For the difference (275 $-$ 270), i.e., 5, the difference in values

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $= \frac{0.079}{10} \times 5 = 0.0395 ≃ 0.04$ (upto three decimal places)

RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics $\sqrt[3]{275} = 6.463 + 0.04 = 6.503$ (upto three decimal places)

Thus, the length of the side of the cube is 6.503 cm.

The document RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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FAQs on RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) - RD Sharma Solutions for Class 8 Mathematics

1. What is the formula to find the volume of a cube?

Ans. The formula to find the volume of a cube is V = s^3, where V is the volume and s is the length of one side of the cube.

2. How can I calculate the cube root of a number without a calculator?

Ans. To calculate the cube root of a number without a calculator, you can use the prime factorization method. Write the number as a product of prime factors, then group the factors into triples and calculate the product of the group. The product will be the cube root of the number.

3. What is the difference between a perfect cube and a cube number?

Ans. A perfect cube is a number that can be expressed as the cube of an integer, while a cube number is any number raised to the power of 3. In other words, all perfect cubes are cube numbers, but not all cube numbers are perfect cubes.

4. How can I find the cube root of a decimal number?

Ans. To find the cube root of a decimal number, you can estimate the cube root by finding the closest whole number and then refine the estimate using the long division method. Divide the decimal number by the cube of the estimated whole number, and repeat the process until you reach the desired level of accuracy.

5. Can a cube have a negative volume?

Ans. No, a cube cannot have a negative volume. Volume is a measure of the amount of space occupied by an object, and it is always a positive value. Therefore, the volume of a cube is always positive, regardless of the sign of its side length.

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RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics PDF Download

Question 1: Making use of the cube root table, find the cube roots 7

Answer 1: Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.By the cube root table, we have:

Question 2: Making use of the cube root table, find the cube root 70

Answer 2: Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.By the cube root table, we have:

Question 3: Making use of the cube root table, find the cube root 700

Answer 3: We have:

Question 4: Making use of the cube root table, find the cube root 7000

Answer 4: We have:

Question 5: Making use of the cube root table, find the cube root 1100

Answer 5: We have:

Question 6: Making use of the cube root table, find the cube root 780

Answer 6: We have:

Question 7: Making use of the cube root table, find the cube root 7800

Answer 7: We have:

Question 8: Making use of the cube root table, find the cube root 1346

Answer 8: By prime factorisation, we have:

Question 9: Making use of the cube root table, find the cube root 250

Answer 9: We have:

Question 10: Making use of the cube root table, find the cube root 5112

Answer 10: By prime factorisation, we have:

Question 11: Making use of the cube root table, find the cube root9800

Answer 11: We have:

Question 12: Making use of the cube root table, find the cube root 732

Answer 12: We have:

Question 13: Making use of the cube root table, find the cube root 7342

Answer 13: We have:

Question 14: Making use of the cube root table, find the cube root 133100

Answer 14: We have:

Question 15: Making use of the cube root table, find the cube root 37800

Answer 15: We have:

Question 16: Making use of the cube root table, find the cube root 0.27

Answer 16: The number 0.27 can be written as 27/100.

Question 17: Making use of the cube root table, find the cube root 8.6

Answer 17: The number 8.6 can be written as 86/10.

Question 18: Making use of the cube root table, find the cube root 0.86

Answer 18: The number 0.86 could be written as 86/100.

Question 19: Making use of the cube root table, find the cube root 8.65

Answer 19: The number 8.65 could be written as 865/100.

Question 20: Making use of the cube root table, find the cube root 7532

Answer 20: We have:

Question 21: Making use of the cube root table, find the cube root833

Answer 21: We have:

Question 22: Making use of the cube root table, find the cube root 34.2

Answer 22: The number 34.2 could be written as 342/10.

Question 23: What is the length of the side of a cube whose volume is 275 cm3. Make use of the table for the cube root.

Answer 23: Volume of a cube is given by:

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RD Sharma Solutions for Class 8 Math Chapter 4 - Cubes and Cube Roots (Part-5) | RD Sharma Solutions for Class 8 Mathematics

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Answer 1: Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:

**Question 2: Making use of the cube root table, find the cube root 70**

Answer 2: Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:

**Question 3: Making use of the cube root table, find the cube root 700**

**Question 4: Making use of the cube root table, find the cube root 7000**

**Question 5: Making use of the cube root table, find the cube root 1100**

**Question 6: Making use of the cube root table, find the cube root 780**

**Question 7: Making use of the cube root table, find the cube root 7800**

**Question 9: Making use of the cube root table, find the cube root 250**

**Question 10: Making use of the cube root table, find the cube root 5112**

Question 11: Making use of the cube root table, find the cube root
9800

**Question 12: Making use of the cube root table, find the cube root 732**

**Question 13: Making use of the cube root table, find the cube root 7342**

**Question 14: Making use of the cube root table, find the cube root 133100**

**Question 15: Making use of the cube root table, find the cube root 37800**

**Question 16: Making use of the cube root table, find the cube root 0.27**

**Question 17: Making use of the cube root table, find the cube root 8.6**

**Question 18: Making use of the cube root table, find the cube root 0.86**

**Question 19: Making use of the cube root table, find the cube root 8.65**

**Question 20: Making use of the cube root table, find the cube root 7532**

Question 21: Making use of the cube root table, find the cube root
833

**Question 22: Making use of the cube root table, find the cube root 34.2**

Question 23: What is the length of the side of a cube whose volume is 275 cm³. Make use of the table for the cube root.