# A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #66 # and the height of the cylinder is #5 #. If the volume of the solid is #27 pi#, what is the area of the base of the cylinder?

Area of the base is

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The volume of a cone is given by the formula (V = \frac{1}{3}\pi r^2 h) and the volume of a cylinder is (V = \pi r^2 h). Given that the total volume of the solid is 27π, and the heights of the cone and cylinder are 66 and 5 respectively, we can set up the equation:

[\frac{1}{3}\pi r^2 \times 66 + \pi r^2 \times 5 = 27\pi]

This simplifies to:

[22r^2 + 5\pi r^2 = 27\pi]

Factoring out (\pi r^2):

[\pi r^2 (22 + 5) = 27\pi]

[27\pi r^2 = 27\pi]

[r^2 = 1]

Thus, (r = 1). Since the radius of the cylinder and the cone are equal, the radius of the cylinder is also 1. The area of the base of the cylinder is given by (A = \pi r^2), so substituting (r = 1):

[A = \pi \times (1)^2]

[A = \pi \times 1]

[A = \pi]

Therefore, the area of the base of the cylinder is (π).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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