wafer cone height

Question

The wafer cone shown is to hold 10 in^3 of ice cream when filled to the bottom. The diameter of the cone is 2 inches and the top of the ice cream has a shape of a hemisphere. Find the height h of the cone. (round two decimal places)

Answer 1

V = 10 in^3

V(h,r) = (1/3)hpi(r^2) + (1/2)(4/3)pir^3 with r=1, V=10, solve for h

= 30/pi -2 inches high ice cream cone from bottom tip to hemispherical's top

= 7.55 inches rounded to two decimal places

Answer 2

Draw and label a diagram!

Volume of hemisphere is 0.5 π in³

Volume of cone is hπ / 3 in³

The sum of the two volumes is 10 in³

Can you solve for h and answer?