To find the volume of the remaining amount after carving out the cone, we need to calculate the volume of the cone and then subtract it from the volume of the cylinder.
The formula for the volume of a cylinder is given by:
V_cylinder = πr^2h_cylinder
Given that the volume of the cylinder before carving is 54 in^3, we can solve for the radius and height using the known volume and assuming the radius and height are equal.
54 = πr^2h_cylinder
Since the radius and height are equal, we can substitute h_cylinder = r into the equation:
54 = πr^2(r)
Simplifying the equation:
54 = πr^3
To solve for r, we can divide both sides of the equation by π:
r^3 = 54/π
r^3 ≈ 17.179
Taking the cube root of both sides, we find:
r ≈ 2.710
Now that we have the radius, we can calculate the volume of the cylinder:
V_cylinder = π(2.710)^2(2.710)
V_cylinder ≈ 63.651 in^3
Now, let's calculate the volume of the cone.
The formula for the volume of a cone is given by:
V_cone = (1/3)πr^2h_cone
The height of the cone will be the same as the height of the cylinder since they were carved out from the same structure.
V_cone = (1/3)π(2.710)^2(2.710)
V_cone ≈ 17.875 in^3
Finally, we can find the volume of the remaining amount by subtracting the volume of the cone from the volume of the cylinder:
V_remaining = V_cylinder - V_cone
V_remaining ≈ 63.651 - 17.875
V_remaining ≈ 45.776 in^3
Therefore, the volume of the remaining amount is approximately 45.776 in^3.
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 colon is 54 in 3 what is the volume of the amount remaining
1 answer
1 answer