# geometry

posted by .

A grain storage tank is in the shape of a cylinder covered by half a sphere. The height of the cylinder is 50 feet and its diameter is 80 feet. find the total surface area (including the base) and volume of the tank.

• geometry -

Think of the grain storage tank as two independent, but related, geometric figures for solving this problem. You have a cylinder with only a bottom (no top because it's covered by the half sphere) and a sphere that's cut across the middle (i.e., half sphere).

The surface area formula for a cylinder with no top is pi*r^2 + 2*pi*r*h.

The surface area formula for half a sphere is (1/2)*4*pi*r^2 = 2*pi*r^2.

The volume area formula for a cylinder is pi*r^2*h.

The volume area formula for half a sphere is (1/2)*4/3*pi*r^3 = 3/2*pi*r^3.

Since the diameter is 80 feet, the radius is 1/2 the diameter or 40 feet.

Therefore, the surface area of the grain storage tank is pi*r^2 + 2*pi*r*h + 2*pi*r^2 = 27,632 sq/ft.

The volume of the grain storage tank is pi*r^2*h + 3/2*pi*r^3 = 552,640 cu/ft.

## Similar Questions

1. ### Math

A cylindrical storage tank has a height of 100 feet and a diameter of 10 feet. (Use pi = 3.14) What is the lateral surface area of the tank?
2. ### Math

A cylindrical storage tank has a height of 100 feet and a diameter of 10 feet. (Use pi = 3.14) What is the lateral surface area of the tank?
3. ### Geometry

A wooden cylinder with a diameter of 10 centimeters and a height of 20 centimeters rests on its circular base. It is cut in half horizontally. What is the difference between the combined surface areas of the two newly created cylinders …
4. ### Geometry

A right cylinder has a radius of 2 feet and a height of 5 feet. Find the surface area of the cylinder. What formula should I be using ?
5. ### college algebra

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and volume of the tank is 5pie cubic feet. Find, to the nearest thousandth of a foot the length of the radius x.
6. ### math

This is the Crailsheim water tower in Baden-Württemberg, Germany. Its construction was completed in 1912. The base of the tower is a graduated cylinder about 19.2 m high with a diameter of 11.5 m at the base and 8.1 m at the top. …
7. ### MATH WORD PROBLEM HELP PLEASE

A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of 320pi cubic feet. What is the diameter, in feet, of the water tank?
8. ### ALGEBRA 2 HONORS

A container is to be made in the shape of a cylinder with a conical top. The lateral surface areas of the cylinder and cone are S1 = 2(pi)rh and S2 = 2(pi)r√(r^2 + h^2). The surface area of the base of the container is B= (pi)r^2. …
9. ### Geometry

A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume …
10. ### Geometry

A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume …

More Similar Questions