The formula for finding the volume of a cone is \large V=\frac{1}{3}\pi r^2h. The volume of a cone is 300 cm^3 and the height is approximately 11.5 cm, what is the approximate radius of the cone?
a
9 cm
b
3 cm
c
29 cm
d
5 cm
c
29 cm
g
The robot's answer is wrong as usual
V = (1/3) π r^2 h
using our given:
300 = (1/3)π r^2 (11.5)
78.26087 = π r^2
r^2 = 24.9112..
r = 4.991... or appr 5
To find the approximate radius of the cone, we need to rearrange the formula for the volume of a cone and solve for the radius. The formula for the volume of a cone is:
V = (1/3)πr^2h
Given that the volume of the cone is 300 cm^3 and the height is approximately 11.5 cm, we can substitute these values into the formula:
300 = (1/3)πr^2(11.5)
To solve for the radius, we'll rearrange the formula:
r^2 = (3 * 300) / (π * 11.5)
Simplifying further:
r^2 ≈ 781.74
To find the approximate value of the radius, we'll take the square root of both sides:
r ≈ √(781.74)
Thus, the approximate value of the radius is approximately 27.95 cm.
None of the given answer choices matches this approximate radius.