Find the volume of a barber's pole having the shape of a right circular cylinder of radius 5 in. and height 29 in. topped by a sphere of the same radius. Round to the nearest tenth, if necessary.

volume= pi*5^2*29 + 4/3 PI 5^3

To find the volume of the barber's pole, we need to calculate the volume of both the cylinder and the sphere, and then add them together.

The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h, where 'r' is the radius and 'h' is the height.

Given that the radius of the cylinder is 5 in. and the height is 29 in., we can substitute these values into the formula:

V_cylinder = π * (5^2) * 29
V_cylinder = π * 25 * 29
V_cylinder ≈ 2269.9 in^3 (rounded to the nearest tenth)

The volume of a sphere is given by the formula: V_sphere = 4/3 * π * r^3, where 'r' is the radius.

Given that the radius of the sphere is also 5 in., we can substitute this value into the formula:

V_sphere = 4/3 * π * (5^3)
V_sphere = 4/3 * π * 125
V_sphere ≈ 523.6 in^3

To find the total volume of the barber's pole, we add the volume of the cylinder and the volume of the sphere:

Total volume ≈ V_cylinder + V_sphere
Total volume ≈ 2269.9 + 523.6
Total volume ≈ 2793.5 in^3 (rounded to the nearest tenth)

Therefore, the volume of the barber's pole is approximately 2793.5 cubic inches.