Question

Jaden is comparing two cones. The radius of the base of cone AA is twice as large as the radius of the base of cone BB. The height of cone BB is twice the height of cone AA. The volume of cone AA is

Answer 1

VA = 2/3πrB²hB

Explanation:

Let the volume of cosA ad cone B be expressed as;

Va = 1/3πra²ha

Vb = 1/3πrb²hb

If the radius of the base of cone A is twice as large as the radius of the base of cone B

rA = 2rB

If the height of cone B is twice the height of cone A, then;

hB = 2hA

hA = hB/2

Recall that;

VA = 1/3πrA²hA

VA = 1/3π(2rB)²(hB/2)

VA = 1/3π*4rB²(hB/2)

VA = 2/3πrB²hB

This gives the volume of cone A