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3 years ago

PLEASE help me solve this problem. I really need help.

Mathematics

1 answer:

mote1985 [20]3 years ago

3 0

When:
a = b = 0 we have point (0,0).
a = 0 and b ≠ 0 vertical line segment from (0, -b) to (0, b)
a ≠ 0 and b = 0 horizontal line segment from (-a, 0) to (a, 0)
a ≠ 0 and b ≠ 0 a ≠ b ellipse
a ≠ 0 and b ≠ 0 a = b circle

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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

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Step-by-step explanation:

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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 8 inches and the height is 12 inches.

The volume of the cone: $\frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.14) (8^{2}) (12)= 803.84$ 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).

Here the radius is 8 inches. We take π as 3.14.

The volume of a full sphere $= \frac{4}{3} \pi r^{3} = \frac{4}{3} (3.14) (8^{3} ) = 2,143.573$ cubic inches.

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The total volume = The volume of the cone + The volume of the half sphere,

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