CONTEXT FOR PHOTO:A hemisphere is placed on top of an inverted cone. The back of the circumference, the radius, and the perpendicular height of the cone are marked with dashed lines. The radius and the height make a right angle and are perpendicular.

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 m3. What is the volume of the whole object?(1 point)
Responses

36 m^3
36 m cubed

24 m^3
24 m cubed

There is not enough information to say.

18 m^3

Answer 1

The volume of the whole object can be calculated by adding the volume of the hemisphere and the volume of the cone together.

To find the volume of the cone, we can use the formula V = (1/3)πr^2h. Since the volume of the cone is given as 12 m^3 and the height is equal to the diameter of the hemisphere, we can substitute these values into the formula.

12 = (1/3)πr^2(d)
12 = (1/3)πr^2(2r)
12 = (2/3)πr^3

Simplifying further, we get:
36 = πr^3
r^3 = 36/π
r^3 ≈ 11.46
r ≈ 2.28

Now that we know the radius of the hemisphere, we can find its volume using the formula V = (2/3)πr^3.

V = (2/3)π(2.28)^3
V ≈ 31.01 m^3

Therefore, the volume of the whole object (hemisphere + cone) is approximately 31.01 m^3.

Answer 2

Please only use the responses as answer

Answer 3

24 m^3