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

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

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