The document Extra Questions- Cubes and Cube Roots Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.

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**Question 1:** Show that –1728 is a perfect cube. Also, find the number whose cube is –1728.

**Solution:** We have

i.e. 1728 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3

⇒ 1728 = 2^{3} * 2^{3} * 3^{3}

⇒ 1728 = (2 * 2 * 3)^{3}

⇒ ∛1728 = 2 * 2 * 3 = 12

Since 1728 is a perfect cube.

∴ –1728 is also a perfect cube.

Also ∛-1728 = –12

⇒ –1728 is a perfect cube of –12.

**Question 2:** Is 216 a perfect cube? What is the number whose cube is 216?

**Solution:** We have

i.e. Resolving 216 into prime factors we have:

216 = 2 * 2 * 2 * 3 * 3 * 3

i.e. 216 can be resolved in to such prime factor which can be grouped into triple of equal of factor and no factor is left over.

∴ 216 is a perfect cube.

Now, 216 = 2^{3} * 3^{3}

⇒ 216 = (2 x 3)^{3} = 6^{3}

⇒ ∛216 = ∛6^{3}

⇒ ∛216 = 6

Thus, the required number is 6, whose cube is 216.

**Question 3: **What is the smallest number by which 288 must be multiplied so that the product is a perfect cube?

**Solution:** Resolving 288 in to prime factors, we have

i.e. 288 = 2 * 2 * 2 * 2 * 2 * 3 * 3

Grouping the factors in triples, we get

288 = [2 * 2 * 2] * 2 * 2 * 3 * 3

We observe that if 288 is multiplied by (2 * 3), then its prime factors will exist in triples. Thus, the required smallest number by which 288 be multiplied to make it a perfect cube is (2 * 3), i.e. 6.

**Question 4:** Find the cube of 4/5.

**Solution:** We have

= 64/25

Thus,

**Question 5: **Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.

**Solution: **We have

0.001728 = 1728/1000000

∴

∴

⇒

⇒

Thus, 0.001728 is the cube of 3/25.

**Question 6:** The volume of a cubical box is 64 cm^{3}. What is its side?

**Solution:** Let ‘x’ be the side of the cube.

∴ x^{3} = 64

or

⇒

= 2 x 2 = 4

**Question 7:** If the surface area of a cube is 486 cm^{2}. Find its volume.

**Solution: **A cube has 6 equal surfaces.

Let side of the cube be x.

∴ Area of a surface = x^{2}

∴ Area of the given cube = 6x^{2}

∴ 6x^{2} = 486

⇒ x^{2} = 486/6 = 81

⇒ x= √81 = 9

∴ x^{3} = 9 * 9 * 9 = 729

Thus, the volume of the given cube = 729 cm^{3}.

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