Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AA 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)%0D%0AResponses
In the image, we see a cylinder with a cone carved out of it. Both the cylinder and the cone have the same radius and height.
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 a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Since the cylinder and the cone have the same radius and height, the volume of the cylinder before removing the cone is 54 in.3.
Let's assume the volume of the cone is Vc.
Therefore, the volume of the amount remaining (Vr) can be calculated as:
Vr = Vc = 54 in.3 - Vc
Now, let's find the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Since the cone and the cylinder have the same radius and height, we can use the same values for r and h.
Vc = (1/3)πr^2h = (1/3)πr^2h = (1/3)π(1)^2(1) = (1/3)π
Now, substitute this value of Vc into the formula for Vr:
Vr = 54 in.3 - (1/3)π
Therefore, the volume of the amount remaining is 54 in.3 - (1/3)π, or whatever the numerical value is.