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
3 cm
b
29 cm
c
5 cm
d
9 cm
d
9 cm
To find the approximate radius of the cone, we can rearrange the formula for the volume of a cone and solve for the radius.
The formula for finding the volume of a cone is:
V = (1/3) * π * r^2 * h
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) * π * r^2 * 11.5
Now, we can rearrange the equation to solve for the radius (r):
r^2 = (3 * 300) / (π * 11.5)
r^2 = 900 / (π * 11.5)
r^2 ≈ 24.6826
To find the approximate radius, we can take the square root of both sides:
r ≈ √24.6826
r ≈ 4.97 cm
Therefore, the approximate radius of the cone is approximately 5 cm (option c).
To find the approximate radius of the cone, we can rearrange the volume formula and solve for r.
The given formula is V = (1/3)πr^2h, where V represents the volume, r represents the radius, and h represents the height.
Substituting the given values, we have 300 = (1/3)πr^2(11.5).
To find the approximate radius, we need to isolate r.
Dividing both sides by (1/3)π(11.5) gives:
r^2 = (300) / ((1/3)π(11.5))
r^2 ≈ 26.09
Taking the square root of both sides, we find that r ≈ √26.09, which is approximately 5.11 cm.
Therefore, the approximate radius of the cone is 5 cm.
So, the correct answer is c) 5 cm.