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 cylinder = pi r^2 h
= pi * 5^2 * 29
= pi * 725
volume sphere - (4/3) pi r^3
= pi * 4/3 * 5^3
= pi * 500/3
and you can finish
write a function for a volume of a cube find the volume of a cube with a side 13.5m long
To find the volume of the barber's pole, we need to calculate the volume of the cylinder and the volume of the sphere, and then add them together.
The volume of a right circular cylinder is given by the formula:
V_cylinder = π * r^2 * h
where π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height of the cylinder.
Substituting the given values, we have:
V_cylinder = π * (5 in)^2 * 29 in
≈ 3.14159 * 25 in^2 * 29 in
≈ 2273.2425 in^3 (rounded to the nearest ten-thousandth)
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
Using the same values for the radius, we can calculate the volume of the sphere:
V_sphere = (4/3) * 3.14159 * (5 in)^3
≈ (4/3) * 3.14159 * 125 in^3
≈ 523.5988 in^3 (rounded to the nearest ten-thousandth)
Now, we can add the volumes of the cylinder and the sphere to find the total volume of the barber's pole:
V_total = V_cylinder + V_sphere
≈ 2273.2425 in^3 + 523.5988 in^3
≈ 2796.8413 in^3 (rounded to the nearest ten-thousandth)
Therefore, the volume of the barber's pole is approximately 2796.8413 cubic inches.