Question

A solid gold cube with edge of 2" is melted down and recast as a cone with a 3" radius base. Find the height of the cone.

8/(9)
2
8/(3)

Answer 1

The height of the cone is three. The volume of the two is 8 inches cubed. 8=3*1/3*x. 8=1x. 8=x.

Answer 2

The height of the cone is
`(8)/(3\pi)`

Explanation:

step 1

Find the volume of the cube

The volume of a cube is equal to

`V=b^(3)`

where

b is the length side of the cube

we have

`b=2\ in`

substitute

`V=2^(3)=8\ in^(3)`

step 2

Find the height of the cone

The volume of the cone is equal to

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

we have

`r=3\ in`

`V=8\ in^(3)` -----> the volume of the cone is equal to the volume of the cube

substitute the values and solve for h

`8=(1)/(3)\pi (3^(2))h`

`8=3 \pi h`

`h=(8)/(3\pi)`