Question

A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters. The height of the container is __centimeters. If its diameter and height were both doubled, the container's capacity would be__ times its original capacity.

Answer 1

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ANSWER #1

To find the volume of a cone, you multiply the base by the height and then divide it by three. So, to find the height, we will do it backwards. First, we will multiply by three.

120π×3=360π

Now, we need to divide by the area of the base. To find the area of the base (a circle) you square the radius and multiply it by pi. The radius is half of the diameter, so since the diameter is 12, the radius is 6.

We square six.

6²=36

We multiply by π.

36π

Now, we can divide our 360π by the area of the base.

360π÷36π=10

Therefore, the height is 10 centimeters.

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ANSWER #2

Let's find the volume of this doubled container. Our height will be twenty this time and the diameter will be 24, so the radius will be 12.

First let's find the area.

12²π

144π

Now we multiply by the height.

144π×20=2880π

And then we divide by three.

2880π÷3=960π

Now we divide this by the volume of our original container to see how many times bigger it is.

960π÷120π=8

Therefore, the container's capacity would be 8 times its original capacity.

Have a wonderful day! :D