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The volume of a right cone is
3750 pi units
^(3). If its circumference measures
30 pi units, find its height.
Answer: units

The volume of a right cone is $3750 \pi$ units $^{3}$ . If its circumference measures $30 \pi$ units, find its height. $\newline$ Answer: units

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Scale drawings: word problems

Full solution

Q. The volume of a right cone is

3750 \pi

units

^{3}

. If its circumference measures

30 \pi

units, find its height.

\newline

Answer: units

Find Radius of Base: First, let's find the radius of the base of the cone using the circumference. The formula for the circumference of a circle is $C = 2 \cdot \pi \cdot r$ , where $C$ is the circumference and $r$ is the radius. $\newline$ Given the circumference is $30 \pi$ units, we can set up the equation: $\newline$ $30 \pi = 2 \cdot \pi \cdot r$
Calculate Radius: Now, we solve for $r$ by dividing both sides of the equation by $2 \times \pi$ : $r = \frac{30 \pi}{2 \times \pi}$ $r = 15$ units
Use Volume Formula: Next, we use the formula for the volume of a cone, which is $V = \frac{1}{3} \pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height. $\newline$ We know the volume is $3750 \pi$ units $^3$ , so we can plug in the values we have: $\newline$ $3750 \pi = \frac{1}{3} \pi (15)^2 h$
Simplify Radius Calculation: To find the height $h$ , we first simplify $(15)^2$ : $(15)^2 = 225$ Now we substitute this back into the volume equation: $3750 \pi = \left(\frac{1}{3}\right) * \pi * 225 * h$
Cancel Pi: Next, we can cancel the pi on both sides of the equation: $3750 = \left(\frac{1}{3}\right) \times 225 \times h$
Find Height: Now, we solve for $h$ by multiplying both sides by $3$ and then dividing by $225$ :
$h = (3750 \times 3) / 225$
$h = 11250 / 225$
$h = 50$ units

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