To find the volume of the remaining amount, we need to subtract the volume of the cone from the volume of the cylinder.
Given that the volume of the cylinder before removing the cone is 54in³, we can find the radius and height of the cylinder. Since the cylinder and cone share the same radius and height, we can use the volume formula for a cylinder, which is given by:
Volume of a cylinder = π * radius^2 * height
Let's assume the radius of the cylinder is r and the height is h.
Therefore, we have:
π * r^2 * h = 54
Now, let's find the volume of the cone. The volume of a cone is given by the formula:
Volume of a cone = 1/3 * π * radius^2 * height
Since the cone and cylinder share the same radius and height, we have:
Volume of the cone = 1/3 * π * r^2 * h
To find the volume of the remaining amount, we subtract the volume of the cone from the volume of the cylinder:
Volume of the remaining amount = Volume of the cylinder - Volume of the cone
= (π * r^2 * h) - (1/3 * π * r^2 * h)
= (2/3) * π * r^2 * h
Therefore, the volume of the remaining amount is equal to (2/3) * π * r^2 * h.
A sculptor created a design by carcung a cone out of a cylinder the cinema and cylinder share the same radius and height if the volume of the cylinder before removing the cone is 54in³ what is the volume of the amount remaining
1 answer
1 answer