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**VOLUME OF CUBE, CUBOID AND CYLINDER****TRY THESE ****Question: **Find the volume of the following cuboids.

Solution: (i) Base area = 8 cm * 3 cm

Height = 2 cm

∴ Volume of the cuboid = (8 cm * 3 cm) * 2 cm = 48 cm^{3}

(ii) Base area = 24 m^{2}

Height = 3 cm

∴ Volume of the cuboid = Base area * height

Cube: Cube is a special case of a cuboid such that its Length = Breadth = Height

∴ Its volume = Edgs * Edge * Edge**Question:** Find the volume of the following cubes (a) with a side 4 cm and (b) with a side 1.5 m.

Solution: (a) Side (edge) of the cube = 4 cm

∴ Volume of the cube = (Edge)3 = (4 cm)^{3}

= 4 * 4 * 4 cm^{3} = 64 cm^{3}

(b) Side (edge) of the cube = 1.5 m

∴ Volume of the cube = (Edge)^{3}

**SOLUTION TO THINK, DISCUSS AND WRITE****Question:** A company sells biscuits. For packing purpose they are using cuboidal boxes; box A → 3 cm * 8 cm * 20 cm, box B → 4 cm * 12 cm * 10 cm. What size of the box will be economical for the company? Why? Can you suggest any other size (dimensions) which has the same volume but is more economical than these?**Solution:**

Clearly, Volume of box B = Volume of box A, but its surface area is less, so its more economical

for the company.

Another size: 8 cm * 6 cm * 10 cm

∵ Volume = 8 * 6 * 10 cm^{3} = 480 cm^{3}

Surface area = 2[(8 * 6) + (6 * 10) + (8 * 10)] cm^{2}

= 2[48 + 60 + 80] cm^{2}

= 2[188] cm^{2} = 376 cm^{2}

Since its surface area is still less than the box B.

∴ It is more economical for the company.**Cylinder:****TRY THESE ****Question:** Find the volume of the following cylinders.**Solution:** (i) Radius (r) = 7 cm

Height (h) = 10 cm

∴ Volume of the cylinder = πr^{2}h

(ii) Base area = 250 m^{2}

Height = 2 m

∴ Volume of the cylinder = Base area * Height

= 250 m^{2} * 2 m = 500 m^{3}**REMEMBER**

(i) 1 cm^{3 }= 1 mL

(ii) 1 litre = 1000 cm^{3 }

(iii) 1 m^{3} = 1000000 cm^{3 } = 1000 mL**EXERCISE 11.4****Question 1. **Given a cylindrical tank, in which situation will you find surface area and in which situation volume.

(a) To find how much it can hold.

(b) Number of cement bags required to plaster it.

(c) To find the number of smaller tanks that can be filled with water from it.**Solution:** (a) Volume (b) Surface area (c) Volume**Question 2.** Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?**Solution: **In volume of a cylinder, the radius is multiplied by squaring it.

∴ Volume of cylinder B will be more than that of A.

Volume of cylinder A

Radius (r) Height (h) = 14 cm

∴ Volume of a cylinder A = πr^{2}h

Volume of cylinder B

Height (h) = 7 cm

∴ Volume of the cylinder B = πr^{2}h

Thus, cylinder B has greater volume.

Now,

Surface area of cylinder A = 2 * π * r * (r + h)

Surface area of cylinder B = 2πrh(r + h) =

= 2 * 22 * [14] cm^{2}

= 616 cm^{2}

Thus, the cylinder of greater capacity has greater (more) surface area.**Question 3.** Find the height of a cuboid whose base area is 180 cm^{2} and volume is 900 cm^{3}.**Solution:** Let the height of the cuboid = h cm

∴ Base area * Height = Volume

or 180 * h = 900

or

Hence, the required height of the cuboid = 5 cm**Question 4.** A cuboid is of dimensions 60 cm * 54 cm * 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?**Solution:** Volume of the cuboid = 60 cm * 54 cm * 30 cm

= (60 * 54 * 30) cm^{3}

Volume of the small cube = (6 * 6 * 6) cm^{3}

= 10 * 9 * 5 = 450

Thus, 450 small cubes can be placed in the given cuboid.**Question 5. **Find the height of the cylinder whose volume is 1.54 m^{3 }and diameter of the base is 140 cm.**Solution: **Diameter = 140 cm ⇒ Radius (r)

Let height of the cylinder be h m.

∴ Volume = πr^{2}h

Since, volume of the cylinder is 1.54 m^{3}.

∴ 22 * 10 * 70 * h = 1.54 * 1000000 = 1540000

or

**Question 6.** A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres

that can be stored in the tank?**Solution:** Radius = 1.5 m =

Height = 7 m

∴ Volume of the tank = πr^{2}h

∵ 1 m^{3 }= 1000 litres

∴ Quantily of milk in the tank = 49.5 x 1000 litres

**Question 7.** If each of a cube is doubled,

(i) How many times will its surface area increase?

(ii) How many times will its volume increase?**Solution:** Let the original edge = x

∴ Increased edge = 2x

(i) ∴ Original S.A. = 6x^{2}

Increased S.A. = 6(2x)^{2} = 24x^{2}

Since,

∴ Surface area is increased by 4 times.

(ii) Original volume = x^{3}

Increased volume = (2x)^{3 }= 8x^{3}

∴ Volume is increased by 8 times.**Question 8.** Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m^{3}, find the number of hours it will take to fill the reservoir.**Solution:** Volume of the reservoir = 108 m^{3}

∵ 1 m^{3} = 1000 litres

∴ Capacity of the reservoir = 108 * 1000 litres

= 108000 litres

Amount of water poured in 1 minute = 60 litres

∴ Amount of water to be poured in 1 hour = 60 * 60 litres

Thus, number of hours required to fill the reservoir =

∴ The required number of hours = 30

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