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Mathematics

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Sindrei [870]3 years ago

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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

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).