Question

MEDAL & FAN

I've been trying to solve this problem for the last hour. Can someone please help explain how to solve it?? Thank you! :)

A solid metal sculpture in Kamila’s backyard is in the shape of a sphere and has a radius of 6 inches. She wants to have it melted and made into small solid cones. She would like the cones to each have a diameter of 6 inches and a height of 9 inches. With these dimensions, how many cones can be made from the metal sphere?

Answer 1

@Hero @robtobey @satellite73

Answer 2

the volume of a sphere with radius \(r\) is \[V=\frac{3}{4}\pi r^3\] which in your case is
\[V=\frac{3}{4}\times 216\times \pi\] or
\[V=162\pi\]

Answer 3

now we need the volume of a cone with radius 3 and height 9, which i believe is \[\pi r^2h=\pi\times 3^2\times 9=81\pi\]

Answer 4

and finally we need to divide

Answer 5

you get 2, pretty much in your head

Answer 6

\[\frac{162\pi}{81\pi}=2\]

Answer 7

Thank you! ILYSM <3 i would fan, but I am already ur fan :)