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
36 m3
36 m cubed
There is not enough information to say.
There is not enough information to say.
24 m3
24 m cubed
18 m3
the answers.
1. cone = cylinder-sphere
2. 24 cm
3. 50/3 TTcm^3
4. 36 in
5. 24 m
To find the volume of the entire object, we need to find the volume of the cone and the volume of the hemisphere separately and then add them together.
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. In this case, the volume of the cone is 12 m³.
We are given that the height of the cone is equal to the diameter of the hemisphere. Since the radius of the hemisphere is half its diameter, we can say that the radius of the cone is also half the height of the cone.
Let's assume the height of the cone is h. Then, the radius of the cone is h/2.
Substituting these values into the volume formula, we get 12 = (1/3)π(h/2)²h.
Simplifying this equation, we get 12 = (1/3)π(h²/4)h.
Multiplying both sides by 3/π to isolate h, we get h³ = 48/π.
To find the volume of the entire object, we need to find the volume of the cone (12 m³) and the volume of the hemisphere.
The volume of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius. In this case, the radius of the hemisphere is the same as the radius of the cone, which is h/2.
Substituting this value into the volume formula, we get V = (2/3)π(h/2)³.
Simplifying this equation, we get V = (2/3)π(h³/8).
Substituting the value of h³ from the previous equation, we get V = (2/3)π(48/π/8).
Simplifying further, we get V = (2/3)(48/8).
Simplifying this equation, we get V = 6.
Therefore, the volume of the entire object is 12 m³ + 6 m³ = 18 m³.
Therefore, the answer is 18 m³.