Question

The circumference of the great circle of a sphere is 24 pi . what is the volume of the sphere ?

Answer 1

`V=7238.2` cubic units

Explanation:

As

• The circumference of the great circle of a sphere is 24 pi.

And we know that the circumference of a great circle = 2
`\pi`r

2
`\pi`r = 24
`\pi`

`\mathrm{Divide\:both\:sides\:by\:}2\pi`

`(2\pi r)/(2\pi )=(24\pi )/(2\pi )`

`r=12`

Using the formula to find the volume of the sphere

`V\:=(4)/(3)\pi r^3`

`V\:=(4)/(3)\pi \left(12\right)^3`

`\mathrm{Multiply\:fractions}:\quad \:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

`V=(4\pi 12^3)/(3)`

`=(2^6\cdot \:3^3\cdot \:4\pi )/(3)` ∵
`\mathrm{Factor}\:12^3:\quad 2^6\cdot \:3^3`

`\mathrm{Cancel\:the\:common\:factor:}\:3`

`V=2^6\cdot \:3^2\cdot \:4\pi`

`V=3^2\cdot \:64\cdot \:4\pi`

`V=64\cdot \:9\cdot \:4\pi`

`V=2304\pi`

`V=7238.2` cubic units