If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π. Is the given statement true or false and justify your answer.

Solution:

Given, a sphere is inscribed in a cube

The ratio of the volume of the cube to the volume of the sphere will be 6 : π

We have to determine if the given statement is true or false.

Volume of cube = a³

Where a is the edge of the cube

Given, sphere is inscribed in a cube

Radius of sphere = a/2

Volume of the sphere = 4/3 πr³

Where, r is the radius of the sphere

= 4/3 π(a/2)³

= 4/3 π(a³/8)

= 1/6 πa³

Ratio of the volumes = volume of cube / volume of sphere

= a³ / 1/6 πa³

= 6/π

Required ratio = 6 : π

Therefore, the given statement is true.

✦ Try This: The length of diagonal of a cube is 15√2 cm, then the length of its side is-

Given, the length of diagonal of a cube is 15√2 cm

We have to find the length of the side of the cube

Diagonal of the cube = a√3

Where, a is the length of the side of the cube

Given, a√3 = 15√2

a = 15√2/√3

= (3×5)√2 / √3

= (√3 × √3 × 5)√2 / √3

= (√3 × 5)√2

= 5(√3 × √2)

= 5√6 cm

So, a = 5√6 cm

Therefore, the the length of the side of the cube is 5√6 cm

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

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NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 9

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π. Is the given statement true or false and justify your answer.

Summary:

The given statement “If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π” is true

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