Question

The volume of the cone is 462 yd.³ The height is 3ft. What is the radius of the cone? use 22/7 for pie

Answer 1

We are asked to determine the radius of a cone given its volume and its height. To do that we will use the following formula for the volume of a cone:

$V=\frac{\pi r^2h}{3}$

Now, we solve for the radius "r". First, we multiply both sides by 3:

$3V=\pi r^2h$

Now, we divide both sides by pi and the height:

$\frac{3V}{\pi h}=r^2$

Now, we take the square root to both sides:

$\sqrt{\frac{3V}{\pi h}}=r$

Now, we convert the height from feet to yards using the following conversion factor:

$1\text{ yd}=\text{ 3ft}$

Multiplying by the conversion factor we get that the height is 1 yd:

Now, we substitute the values:

$\sqrt{\frac{3(462yd^3)}{(\frac{22}{7})(1yd)}}=r$

Solving the operations:

$21yd=r$

Therefore, the radius is 21 yd.