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