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 share the same height and radius, we can simplify the formula to V = πr^2h/3 for the cone.
Given that the volume of the cylinder before removing the cone is 54 in^3, we can set up the equation:
54 = πr^2h
To find the volume of the remaining amount, we need to subtract the volume of the cone from the volume of the cylinder.
The volume of the cone is given by V_cone = πr^2h/3.
Substituting the value of h from the equation above, we get V_cone = πr^2(54/π)/3 = 18r^2.
The volume of the remaining amount is then given by V_remaining = V_cylinder - V_cone = 54 - 18r^2.
Since we know that both the cone and cylinder share the same radius and height, we can rewrite the equation as V_remaining = 54 - 18r^2.
To find the volume of the remaining amount, we need to know the value of r. Without that information, we cannot determine the exact volume. Therefore, none of the given options (27 in^3, 36 in^3, 40 in^3, 18 in^3) can be selected as the correct answer.
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
27 in.3
27 in. cubed
36 in.3
36 in. cubed
40 in.3
40 in. cubed
18 in.3
1 answer