Question

The perimeter of the largest cross section of a sphere is 88 centimeters.

Find the radius and volume of the sphere.

Answer 1

The radias would be 14 and the volume would be 11507.924943185202. I'm not that sure on these. Tell me if these are correct plz.

Answer 2

Radius of the sphere is 14 cm and Volume of the sphere is 1498.7 cm³.

Explanation:

Given Perimeter of the largest cross section of the sphere = 88 cm.

We have to find Radius of the sphere and Volume of the sphere.

We know that Largest Cross section of the sphere is a circle whose radius is same as of sphere.

let r be the radius of cross sectional circle or sphere.

Now,

Circumference of circle = 88 cm

2πr = 88

`r=88*(7)/(2*22)`

r = 2 × 7

r = 14 cm

Volume of the sphere =
`(4)/(3)\pi r^3`

=
`(4)/(3)*(22)/(7)*14^3`

=
`(4)/(3)*22*14^2*2`

= 11498.7 cm³

Therefore, Radius of the sphere is 14 cm and Volume of the sphere is 1498.7 cm³.