# A propane tank is in the form of a cylinder with two half-spheres, one on each end. The radius of the cylinder is the same as the radius of each half-sphere. What is the volume of a propane tank of cylindrical length 12 ft and radius 5 ft, correct to the nearest whole cubic foot?

13 years ago

7 months ago

## To find the volume of the propane tank, we need to calculate the volumes of the cylinder and the two half-spheres separately, and then add them together.

First, let's find the volume of the cylinder. The formula for the volume of a cylinder is V_cylinder = Ï€ * r^2 * h, where r is the radius and h is the height.

In this case, the radius of the cylinder is given as 5 ft, and the height is given as 12 ft. Plugging in these values, we get:

V_cylinder = Ï€ * 5^2 * 12 = 300Ï€ ft^3.

Next, let's find the volume of each half-sphere. The formula for the volume of a sphere is V_sphere = (4/3) * Ï€ * r^3, where r is the radius.

In this case, the radius of each half-sphere is also given as 5 ft. Plugging in this value, we get:

V_half-sphere = (4/3) * Ï€ * 5^3 = (4/3) * Ï€ * 125 = 166.667Ï€ ft^3.

Since we have two half-spheres, we need to multiply this volume by 2:

V_total-spheres = 2 * 166.667Ï€ = 333.333Ï€ ft^3.

Finally, let's add the volumes of the cylinder and the two half-spheres together:

V_total = V_cylinder + V_total-spheres = 300Ï€ + 333.333Ï€ = 633.333Ï€ ft^3.

To find the value rounded to the nearest whole cubic foot, we can calculate the numerical value of Ï€ (pi) and round it:

Ï€ is approximately 3.14159, so:

V_total = 633.333 * 3.14159 â‰ˆ 1989.867 ft^3.

Rounding to the nearest whole cubic foot, the volume of the propane tank is approximately 1990 ft^3.