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Kipish [7]
3 years ago
8

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 you

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

Mathematics
2 answers:
almond37 [142]3 years ago
4 0
3.14 x 9^2 x 14/3 = 1186.92

4/3 x 3.14 x 9^3 = 1526.04

1186.92 + 1526.04 = 2712.96  = 2713 cubic inches

timama [110]3 years ago
4 0

Answer: V = 2712.94 cubic inches.

Step-by-step explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.

<u>Volume of Cone:</u>

V₁ = \frac{1}{3}.B.h

B is area of the base

h is height

Since the cone has its base as a circle, the volume will be:

V₁ = \frac{1}{3}.π.r^{2}.h

V₁ = \frac{1}{3} . 3.14 . 9^{2} . 14

V₁ = 1186.9 cubic inches

<u>Volume of Half-Sphere:</u>

V₂ = \frac{2}{3}.π.r^{3}

V₂ = \frac{2}{3} . 3.14 . 9^{3}

V₂ = 1526.04 cubic inches

<u>Total Volume:</u>

V = V₁ + V₂

V = 1186.9 + 1526.04

V = 2712.94 cubic inches

The volume of the prop is V = 2712.94 cubic inches

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