Question

This cone has a volume of 96. What is the height of the cone?

A
B
C
D
E
10 m
8m
9m
12 m
7m
6m

Answer 1

Let's use the formula for the volume of a cone:

Volume = (1/3) * pi * r^2 * h

We know that the volume is 96, but we don't know the radius or the height. We can simplify the formula by solving for h:

h = 3 * Volume / (pi * r^2)

We don't have the radius, but we can use the fact that the volume of a cone is also equal to:

Volume = (1/3) * pi * r^2 * h

We can rearrange this formula to solve for r^2:

r^2 = 3 * Volume / (pi * h)

Now we can substitute this expression for r^2 into the formula for h:

h = 3 * Volume / (pi * r^2)
h = 3 * 96 / (pi * 3 * Volume / pi)
h = 96 / (Volume)

h = 1

Therefore, the height of the cone is 1.

Answer 2

To solve for the height of the cone, we need to use the formula for the volume of a cone, which is:

V = 1/3 * π * r^2 * h

where V is the volume, r is the radius of the base of the cone, h is the height of the cone, and π is a constant equal to approximately 3.14.

We are given that the volume of the cone is 96. Plugging this value into the formula, we get:

96 = 1/3 * π * r^2 * h

We do not have the value of the radius of the cone, so we cannot solve for the height directly. However, we can use the fact that the volume of a cone is equal to 1/3 the volume of a cylinder with the same base and height. The formula for the volume of a cylinder is:

V = π * r^2 * h

Since the cone and cylinder share the same height, we can set the volumes of the cone and cylinder equal to each other:

1/3 * π * r^2 * h = π * r^2 * h

Simplifying the equation:

1/3 = r^2

r = √(1/3)

Now that we have the value of the radius, we can plug it into the original formula for the volume of the cone and solve for the height:

96 = 1/3 * π * (√(1/3))^2 * h

96 = 1/3 * π * 1/3 * h

h = 96 / (1/3 * π * 1/3)

h ≈ 9.05

Therefore, the height of the cone is approximately 9.05. The closest option given is 9m.