Question

A cone has the height 14 centimeters and base with the circumference or 8.4 pi centimeters. What is the volume of the cone in terms of pi.
19.6pi cubic cm
39.2pi cubic cm
82.32pi cubic cm
282.24pi cubic cm

Answer 1

The answer is C.

Here is the formula for volume of cone:

$\frac{1}{3} \pi r^{2} h$

where r is the radius and h is the height.

$\pi r^{2}$ is the area of the "base" or the fomula for calculating the area of a circle.

In your question, the height is given, but you don't know the radius. However, it could be found using the circumference of 8.4pi cm.

The formula for the relationship between circumference, diameter, and the constant pi:

$C =\pi d$

where C is the circumference and d is the diameter of the circle.

Substitute the numbers in:

$8.4 \pi = \pi d$

Remove $\pi$ from both sides of the equation:

$d=8.4$

Diameter is the length across the circle, while radius is half of diameter.

Hence, $r =4.2$

Now that you have all the "information" you need to calculate the cone's volume, substitute the numbers into the formula:

$\frac{1}{3} \pi * 4.2^{2}* 14$

You should get  $82.32\pi cm^{2}$  as your answer. The $\pi$ is left alone because the question stated "in terms of pi", but if that weren't stated pi should be replaced with 22/7 or 3.14 depending on the question.

I hope this clears up any confusion you might have! If not, feel free to leave a comment with your question.