# A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #6 # and the height of the cylinder is #8 #. If the volume of the solid is #20 pi#, what is the area of the base of cylinder?

In order to make things easier to follow, I'm going to use the letters N and L to stand for Cone and Cylinder, respectively.

We know:

What is the size of the cylinder's base?

First, let's enter the values for the volumes of the two shapes into the formulas:

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Given that the solid consists of a cone on top of a cylinder with the same radius, and the volume of the solid is 20π, and the height of the cone is 6 and the height of the cylinder is 8, we can find the area of the base of the cylinder.

The volume of the solid is the sum of the volumes of the cone and the cylinder:

Volume of cone = (1/3)πr^2h Volume of cylinder = πr^2h

Given that the volume of the solid is 20π and the height of the cone is 6, we can set up the equation:

(1/3)πr^2 * 6 + πr^2 * 8 = 20π

Solving this equation for r:

2πr^2 + 6πr^2 = 20π 8πr^2 = 20π r^2 = 20/8 r^2 = 5/2 r = √(5/2)

Now that we have the radius of the cylinder, we can find the area of the base of the cylinder:

Area of base of cylinder = πr^2 Area of base of cylinder = π * (5/2) Area of base of cylinder = (5π)/2

Therefore, the area of the base of the cylinder is (5π)/2 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.

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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- A chord with a length of #5 # runs from #pi/4 # to #pi/2 # radians on a circle. What is the area of the circle?
- A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 8 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?
- How do you use Heron's formula to find the area of a triangle with sides of lengths #2 #, #5 #, and #5 #?

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