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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)

Respuesta :

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.
calculista

Answer:

The height of the cone is [tex]\frac{8}{3\pi}[/tex]

Step-by-step explanation:

step 1

Find the volume of the cube

The volume of a cube is equal to

[tex]V=b^{3}[/tex]

where

b is the length side of the cube

we have

[tex]b=2\ in[/tex]

substitute

[tex]V=2^{3}=8\ in^{3}[/tex]

step 2

Find the height of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=3\ in[/tex]

[tex]V=8\ in^{3}[/tex] -----> the volume of the cone is equal to the volume of the cube

substitute the values and solve for h

[tex]8=\frac{1}{3}\pi (3^{2})h[/tex]

[tex]8=3 \pi h[/tex]

[tex]h=\frac{8}{3\pi}[/tex]

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