Harper is working on a science project where she is studying the properties of cones. She has a cone with a volume of 2, 307.9 mm* and a height of 5 mm. She needs to find the radius of the cone for her project. Can you help Harper find the radius? Use
the formula for the volume of a cone:
Volume = (1/3) * π * r^2 * h
where r is the radius and h is the height.
Given:
Volume = 2,307.9 mm^3
Height = 5 mm
Let's rearrange the formula to solve for r:
Volume = (1/3) * π * r^2 * h
Multiply both sides by 3:
3 * Volume = π * r^2 * h
Divide both sides by π * h:
(3 * Volume) / (π * h) = r^2
Take the square root of both sides to find r:
r = sqrt((3 * Volume) / (π * h))
Now, substitute the given values:
r = sqrt((3 * 2,307.9 mm^3) / (π * 5 mm))
Simplifying:
r = sqrt(6,923.7 mm^3 / 15.7 mm)
r = sqrt(441.206 decor^3)
Therefore, the radius of the cone is approximately 20.99 mm.