# 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 #11 #. If the volume of the solid is #140 pi#, what is the area of the base of the cylinder?

The formula for volume of a cone is

The radius, r, must be determined before we can begin our search for the area of the base.

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The volume ( V ) of the solid consisting of a cone on top of a cylinder is given by ( V = \frac{1}{3} \pi r^2 h_{\text{cone}} + \pi r^2 h_{\text{cylinder}} ), where ( r ) is the radius, ( h_{\text{cone}} ) is the height of the cone, and ( h_{\text{cylinder}} ) is the height of the cylinder. Substituting the given values and solving for ( r ), we find ( r = 3 ). Then, to find the area of the base of the cylinder, we use the formula for the area ( A ) of a circle: ( A = \pi r^2 ). Substituting ( r = 3 ), we find ( A = 9\pi ). Therefore, the area of the base of the cylinder is ( 9\pi ).

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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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