Question

A cone with a volume of 4 in cubed, the diameter of the ice cream is euqal to its height, what is the total volume of ice cream in and on top of the cone? it is a hemisphere

Answer 1

Let the cone have height h and base radius r. Cone volume: V_cone = (1/3)πr^2h = 4. The hemisphere on top has diameter = h, so its radius R = h/2. The hemisphere also sits on the cone, so r = R = h/2.

Compute cone volume in terms of h:
V_cone = (1/3)π(h/2)^2 h = (1/3)π(h^3/4) = (π h^3)/12 = 4.

Hemisphere volume:
V_hemi = (1/2)(4/3)πR^3 = (2/3)π(h/2)^3 = (2/3)π(h^3/8) = (π h^3)/12.

Thus V_hemi = V_cone = 4 in^3, so total ice cream volume = 4 + 4 = 8 in^3.