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

The answer is C.

Here is the formula for volume of cone:

where r is the radius and h is the height.

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:

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

Substitute the numbers in:

Remove from both sides of the equation:

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

Hence,

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

You should get    as your answer. The 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.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq