Question

An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m^3 . What is the volume of the whole object?

A. There is not enough information to say
B. 18m^3
C. 24 m^3
D. 36 m^3

Answer 1

yeah, I got most of them wrong but here's the answers ig

1. cone = cylinder -- sphere
2. 24 cm^3
3. 50/3 π cm^3
4. 36 in.^3
5. 24 m^3

Answer 2

Let's assume the diameter of the hemisphere is D.

Since the height of the cone is equal to the diameter of the hemisphere, the height of the cone is also D.

The formula for the volume of a cone is V_cone = (1/3) * π * r^2 * h, where r is the radius of the base of the cone and h is the height of the cone.

Since the height and diameter of the cone are the same, the radius of the base of the cone is D/2.

Substituting the values into the formula, we have V_cone = (1/3) * π * (D/2)^2 * D.

Given that V_cone = 12 m^3, we can solve for D:

12 = (1/3) * π * (D/2)^2 * D
36 = π * (D/2)^2 * D
36 = π * D^3/4
144 = π * D^3
D^3 = 144/π
D ≈ 5.02

Now, the volume of the hemisphere can be calculated using the formula V_hemisphere = (2/3) * π * r^3, where r is the radius of the hemisphere.

Since the radius of the hemisphere is D/2 ≈ 2.51, we have V_hemisphere = (2/3) * π * (2.51)^3.

The volume of the whole object, V_whole, is the sum of the volume of the hemisphere and the cone:

V_whole = V_hemisphere + V_cone = (2/3) * π * (2.51)^3 + 12.

Calculating the approximate value for V_whole, we get:

V_whole ≈ 24.024 + 12
V_whole ≈ 36.024.

Therefore, the volume of the whole object is approximately 36 m^3.

The answer is D. 36 m^3.

Answer 3

Based on the given correction in the answers, the correct answer for the volume of the whole object is 24 m^3, which matches the answer choice E. 24 m^3.