Question

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

14ich long 9inch wide half of shape with dotted line

Answer 1

1. To solve this problem you must sum the volume of the cone and the volume of the hemisphere. This means that the volumen of the prop is:

Vt=Vc+Vh

Vt is the volumen of the prop.
Vc is the volumen of the cone.
Vh is the volume of the hemisphere.

2. The volume of the cone (Vc) is:

Vc=1/3(πr²h)

r=9 in
h=14 in
π=3.14

4. Then, you have:

Vc=(3.14)(9 in)²(14 in)/3
Vc=3560.76 in³/3
Vc=1186.92

5. The volume of the hemisphere (Vh) is:

Vh=2/3(πr³)

π=3.14
r=9 in

6. Then, you have:

Vh=(2)(3.14)(9 in)³/3
Vh=4578.12 in³/3
Vh=1526.04 in³

7. Finally, the volumen of the prop (Vt) is:

Vt=Vc+Vh
Vt=1186.92 in³+1526.04 in³
Vt=2713.0 in³

What is the volume of the prop?

The volume of the prop is 2713.0 in³