15.) 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.
A) 2276.5 in.3 B) 2799.8 in.3 C) 1046.7 in.3 D) 4553.0 in.3
The volume of a cylinder is V = pi * r^2 * h, and the volume of a sphere is V = (4/3) * pi * r^3.
The volume of the barber pole including the sphere can be found by adding the volume of the cylindrical part to the volume of the spherical part.
You are given that the radius is 5in and the height is 29in. Can you find the volume?
2 parts:
1. the cylinder: V = pi(5^2)(29) = 725pi
2. the cap: V = (4/3)pi(5^3) = (500/3)pi
Evaluate and see which matches your choices
(I got 2801.3 rounded to one decimal, the closest is B), looks like they used 3.14 for pi, a rather primitive choice for pi)
To find the volume of the barber's pole, we need to find the combined volume of the cylinder and the sphere.
First, let's find the volume of the cylinder. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Plugging in the values given:
V_cylinder = π(5^2)(29)
V_cylinder = 725π
Next, let's find the volume of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3. Plugging in the radius of 5 inches:
V_sphere = (4/3)π(5^3)
V_sphere = 500π/3
To find the combined volume, add the volume of the cylinder and the volume of the sphere:
V_total = V_cylinder + V_sphere
V_total = 725π + 500π/3
Now, to round to the nearest tenth, we need to calculate the value numerically:
V_total ≈ 2276.5
Therefore, the volume of the barber's pole is approximately 2276.5 cubic inches.
The correct answer is A) 2276.5 in.3.