Question

See question about volume of cone, half sphere and cone/sphere combined

Answer 1

The volume of the prop rounded to the nearest tenth is 2882.5 in^3

EXPLANATION :

Recal the volume formulas :

Cone :

`V=(1)/(3)\pi r^2h`

Hemisphere/Half sphere :

`V=(2)/(3)\pi r^3`

From the problem, the radius of the cone and half sphere is the same.

The radius is r = 9 in

The height of the cone is 16 in

Using the formulas above :

Cone :

`\begin{gathered} V=(1)/(3)(3.14)(9)^2(16) \\ V=1356.48 \end{gathered}`

Half sphere :

`\begin{gathered} V=(2)/(3)(3.14)(9)^3 \\ V=1526.04 \end{gathered}`

The area of the prop is the sum of these two volumes :

`1356.48+1526.04=2882.52`