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24 December, 07:24

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

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  1. 24 December, 08:56
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    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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