Question

Cone a is 9 inches tall and has a diameter of 8 inches. Cone b has a diameter of 12 inches. What height does cone b need to be in order to hold the same volume as cone A

Answer 1

area of cone = 1/3 r^2 (radius) * pi* height

so, we get diameter = 2 radius,

so radius = 4. so, 4^2 * pi = 16pi. Multiply this by 1/3 then by 9 to get 48 pi as the area of cone a.

Cone b has a diamter of 12. so, the radius is 6, and r^2 = 36. then we get 36pi for the base and multiply this by 1/3 height to get cone a.

so, we get 36pi * 1/3 h(height) = 48pi

so we get 12pi * h = 48 pi

12h = 48

h = 4

This works since the height of b should be smaller as its radius is bigger