Volume of Cones, Cylinders, and Spheres Quick Check
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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
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 volume of the whole object can be found by adding the volume of the hemisphere and the volume of the cone.
The volume of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height.
The volume of a hemisphere is given by V = (2/3)πr^3, where r is the radius.
Given that the volume of the cone is 12 m^3 and the height of the cone is equal to the diameter of the hemisphere, we can find the radius of the cone and the hemisphere.
Since the height of the cone is equal to the diameter of the hemisphere, the radius of the cone is equal to 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.
Since we have the volume of the cone as 12 m^3, we can write the equation as follows:
12 = (1/3)π(h/2)^2h
Solving this equation, we can find the height of the cone. Once we have the height of the cone, we can find the radius of the cone and the hemisphere.
Then, we can calculate the volume of the hemisphere using the radius found, add it to the volume of the cone, and get the volume of the whole object.
Without this information, we cannot determine the volume of the whole object. Therefore, the answer is "There is not enough information to say."