Use the image to answer the question.
A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.
A sculptor created a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume of the cylinder before removing the cone is 54 in.3 , what is the volume of the amount remaining?(1 point)
Responses
40 in.3
40 in. cubed
27 in.3
27 in. cubed
18 in.3
18 in. cubed
36 in.3
36 in. cubed
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The volume of the remaining amount can be found by subtracting the volume of the cone from the volume of the cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Since the cone and cylinder have the same radius and height, we can use the same values for r and h in both formulas.
The volume of the cylinder is given as 54 in.3, so we have:
54 = πr^2h
To find the volume of the cone, we can use the formula V = (1/3)πr^2h since the base of the cone is common with the base of the cylinder.
The volume of the cone is given as (1/3)πr^2h, so we have:
V_cone = (1/3)πr^2h
We can substitute the value of h from the equation for the cylinder:
V_cone = (1/3)πr^2(54/πr^2)
= 18 in.3
Therefore, the volume of the amount remaining is 54 in.3 - 18 in.3 = 36 in.3.
Answer: 36 in.3