Question 41·Medium·Area and Volume

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The circumference of the base of a right circular cylinder is $10\pi$ centimeters. The volume of the cylinder is $1{,}250\pi$ cubic centimeters. Which choice gives the height, in centimeters, of the cylinder?

For a cylinder problem that gives circumference instead of diameter or radius, first use $C=2\pi r$ to find the radius. Then use $V=\pi r^2h$ , cancel common factors such as $\pi$ , and solve for the requested dimension. Keep circumference, base area, and volume separate: they use different formulas and represent different quantities.

Hints

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Find the radius first

Use the circle circumference formula $C=2\pi r$ to find the radius of the cylinder's base.

Use the volume formula

After finding the radius, substitute it into $V=\pi r^2h$ along with the given volume.

Isolate the height

Simplify the squared radius and cancel the common factor of $\pi$ before dividing to solve for $h$ .

Desmos Guide

Find the radius and evaluate the height

In Desmos, enter r=(10*pi)/(2*pi) to calculate the base radius. On the next line, enter (1250*pi)/(pi*r^2) to evaluate the height.

Step-by-step Explanation

Use the circumference formula

The circumference of a circle is $C=2\pi r$ . Since the base circumference is $10\pi$ , write

10\pi=2\pi r.

Divide both sides by $2\pi$ :

r=5.

Write the volume equation

The volume of a right circular cylinder is

V=\pi r^2h.

Substitute $V=1{,}250\pi$ and $r=5$ :

1{,}250\pi=\pi(5)^2h.

Solve for the height

Simplify and divide:

\begin{aligned} 1{,}250\pi&=25\pi h\\ 1{,}250&=25h\\ h&=50 \end{aligned}

The height is 50 centimeters, which is choice (C).

Question 41·Medium·Area and Volume

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation