Question

Use the image to answer the question.

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.

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

There is not enough information to say.
There is not enough information to say.

24 m3
24 m cubed

36 m3
36 m cubed

18 m3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a cone is calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height. Since the volume of the cone is 12 m^3, we can substitute the values to find the radius of the cone.

12 = (1/3) * π * r^2 * h
12 = (1/3) * π * r^2 * 2r
12 = (2/3) * π * r^3
r^3 = 18 / π
r ≈ 2.42 (approximate value)

Now, the total volume of the object is the volume of the cone plus the volume of the hemisphere. The volume of a hemisphere is given by V = (2/3) * π * r^3.

Volume of hemisphere = (2/3) * π * (2.42)^3 ≈ 18.5 m^3

Total volume = Volume of cone + Volume of hemisphere
Total volume ≈ 12 + 18.5 ≈ 30.5 m^3

Therefore, the volume of the whole object is approximately 30.5 m^3.