Question

The volume of a cone is 113.04 mm2. What is the approximate volume of a sphere that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth.

Answer 1

`V=169.56\ mm^3`

Explanation:

we know that

The volume of the cone is given by te formula

`V=(1)/(3)\pi r^(2)h`

we have

`V=113.04\ mm^3`

substitute

`113.04=(1)/(3)\pi r^(2)h`

`339.12=\pi r^(2)h` ----> equation A

Remember that

A sphere has the same height and a circular base with the same diameter

That means----> The diameter of the sphere is equal to the height of the cone and the radius of the sphere is equal to the radius of the base of cone

`r=(h)/(2)`

equation A is equal to

`339.12=\pi ((h)/(2))^(2)h`

`339.12=\pi ((h^3)/(3))`

`1,017.36=\pi h^3` -----> equation B

The volume of the sphere is given by

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

substitute

`V=(4)/(3)\pi ((h)/(2))^(3)`

`V=(4)/(24)\pi h^3`

`V=(1)/(6)\pi h^3`

substitute equation B in the expression above

`V=(1)/(6)(1,017.36)=169.56\ mm^3`