The formula for finding the volume of a cone is \large V=\frac{1}{3}\pi r^2h. The volume of a cone is 500 cm^3 and the height is approximately 13.5 cm, what is the approximate radius of the cone?
a
6 cm
b
19 cm
c
2 cm
d
15 cm
d
15 cm
To find the approximate radius of the cone, we can rearrange the formula for volume \large V=\frac{1}{3}\pi r^2h to solve for the radius.
Dividing both sides of the equation by \frac{1}{3}\pi h, we have:
\large r^2 = \frac{3V}{\pi h}
Plugging in the given values: V = 500 cm^3 and h = 13.5 cm, we get:
\large r^2 = \frac{3(500)}{\pi(13.5)}
\large r^2 = \frac{1500}{13.5\pi}
\large r^2 \approx \frac{35.211}{\pi}
\large r^2 \approx 11.2062
To find the approximate value of the radius, we take the square root of both sides:
\large \sqrt{r^2} \approx \sqrt{11.2062}
\large r \approx 3.347
Therefore, the approximate radius of the cone is 3.35 cm.