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The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?

Respuesta :

Since the height of the pyramid is 3 times the radius of the cone we can express height of the pyramid as a function of radius of the cone.

Let radius of cone = r
Then, height of the pyramid = 3r

Area of the base of the cone = pi x r^2 = area of the pyramid.

If the base dimensions of the pyramid are l and b, then area of the pyramid, l x b = pi x r^2.

The volume of the pyramid = 1/3 x l x b x h

We know, l x b = pi x r^2 and h = 3r.

Thus, volume of pyramid is = 1/3 x pi x r^2 x 3 r = pi x r^3

The volume of the pyramid is πr³ cubic units. Then the correct option is A.

What is the volume of the pyramid?

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (A × H) / 3

V = (L × B × H) / 3

Where, A is the base area of the pyramid.

Let r be the radius of base circle of the cone.

The height of the pyramid in the diagram is three times the radius of the cone.

Then the height of the pyramid will be 3r.

The base area of the pyramid is the same as the base area of the cone.

Base area of pyramid = Base area of cone

Base area of pyramid = πr²

Then the volume of the pyramid will be

Volume of pyramid = (1/3) x  πr² x (3r)

Volume of pyramid = πr² x r

Volume of pyramid = πr³ cubic units

The volume of the pyramid is πr³ cubic units.

Then the correct option is A.

Complete question is attached below.

More about the volume of the pyramid link is given below.

https://brainly.com/question/23302816

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