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sesenic [268]
3 years ago
10

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 y

our answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

Mathematics
1 answer:
Marizza181 [45]3 years ago
5 0
The answer is 2,713 in³

The volume (V) of the prop is the sum of the volume of cone (V1) and half of the volume of the sphere (V2): V = V1 + 1/2 * V2

Volume of the cone is:
V1 = π r² h / 3
According to the image,
h = 14 in
r = 9 in
and
π = 3.14
V1 = 3.14 * 9² * 14 / 3 =  1,186.92 in³

The volume of the sphere is:
V2 = π r³ * 4/3
According to the image,
r = 9 in
and
π = 3.14
V2 = 3.14 * 9³ * 4/3 = 3,052.08 in³

The volume of the prop is:
V = V1 + 1/2 * V2
V = 1,186.92 in³ + 1/2 * 3,052.08 in³
V = 1,186.92 in³  + 1,526.04 in³ 
V = 2,712.96 in³ ≈ 2,713 in³
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You can see how this works by thinking through what's going on.

 

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So there's a pattern.  If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.

 

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