I could really use some help with this problem because I'm pretty confused on what to do.
The formula for the volume of a cone is V=1/3(pi)r^2h where v represents volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
Square r.
66 = 1/3(3.14) 9 h
Combine terms.
66 = 3 * 3.14h = 9.42h
Divide both sides by 9.42.
7 = h
To find the height of the cone, we need to rearrange the formula for volume and solve for h.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V represents volume, r represents the radius of the base, and h represents the height.
Given that the volume (V) is 66 cubic centimeters and the base radius (r) is 3 centimeters, we can substitute these values into the formula and solve for h.
Let's break the formula down step by step:
V = (1/3) * π * r^2 * h
Substituting the given values:
66 = (1/3) * π * 3^2 * h
Now, let's simplify:
66 = (1/3) * π * 9 * h
Next, let's remove the fractions by multiplying both sides of the equation by 3:
66 * 3 = π * 9 * h
Simplifying further:
198 = 9πh
Finally, to solve for h, divide both sides by 9π:
h = 198 / (9π)
Calculating this value, we get:
h ≈ 7.030 centimeters
Therefore, the height of the cone is approximately 7.030 centimeters.