# 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 #9 # and the height of the cylinder is #12 #. If the volume of the solid is #45 pi#, what is the area of the base of the cylinder?

The area is

Total amount

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Since the solid consists of a cone on top of a cylinder, its volume can be expressed as the sum of the volumes of the cone and the cylinder. Given that the volume of the solid is 45π, and the height of the cone is 9 and the height of the cylinder is 12, we can set up the equation:

Volume of cone + Volume of cylinder = 45π

Using the formulas for the volume of a cone (V_cone = (1/3)πr^2h) and the volume of a cylinder (V_cylinder = πr^2h), and substituting the given values:

(1/3)πr^2(9) + πr^2(12) = 45π

Simplify and solve for r:

(3r^2 + 12r^2) = 135 15r^2 = 135 r^2 = 9 r = 3

Now that we have found the radius of the cylinder, we can find the area of its base using the formula for the area of a circle:

Area = πr^2 Area = π(3^2) Area = π(9) Area = 9π

So, the area of the base of the cylinder is 9π square units.

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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.

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