Question

Select the correct answer from each drop-down menu.
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
10
centimeters. If its diameter and height were both doubled, the container's capacity would be
2
times its original capacity.

Answer 1

Hi welcome :)

do you have any ideas what the answer would be?

Answer 2

`A conical container can hold 120π cubic centimeters of water. `

This tells us that the volume of a cone is 120\(\pi\)

The formula for the volume of a cone is
\( V = \dfrac{1}{3} \pi r^2 h\)

They told you that the diameter is 12 cm and that the height is 10 cm. And the volume of this cone would be 120\(\pi\)

Now they're asking you, if you double the diameter and height. How much does the volume increase by?

Remember that the formula has radius.
They gave you the diameter so you need to find the radius.

Radius = Diameter / 2

So the new cone has a diameter of 24 cm and a height of 20 cm. What is the volume of this cone?
(Remember to find the radius and plug that value into the formula)

And then whatever value you get for the volume, divide it by 120\(\pi\) and that will be your final answer - how much the capacity of the cone has increased by doubling the diameter and height