Question

PLEASE HELP!! I NEED THIS TODAY!

You have a wooden cube and a spherical wooden ball.
Both of them have the same volume: exactly 10 cubic inches.
Which one is taller?
Use the volume formulas. Show your work.

Answer 1

The sphere is taller than the cube

Explanation:

we know that

The height of the cube is equal to the length side of the cube and the height of the sphere is equal to the diameter of the sphere

step 1

Find the length side of the cube

we know that

The volume of the cube is equal to

`V=b^(3)`

where

b is the length side of the cube

we have

`V=10\ in^(3)`

substitute and solve for b

`10=b^(3)`

`b=\sqrt[3]{10}\ in`

`b=2.15\ in`

step 2

Find the diameter of the sphere

we know that

The volume of the sphere is equal to

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

we have

`V=10\ in^(3)`

substitute and solve for r

`10=(4)/(3)\pi r^(3)`

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

`r=\sqrt[3]{(30)/(4\pi)}`

`r=1.34\ in`

Find the diameter

`D=2r=2*1.34=2.68\ in`

step 3

Compare

`2.68\ in > 2.15\ in`

therefore

The sphere is taller than the cube