Question

Could use some help with these. They r confusing!!

Farmer Hanson is considering installing a new grain bin on his farm. Before making the purchase he needs to know the capacity of the bin (how much grain the bin will hold). He sees there are two parts: a tapered top part that comes to a point and a “straight” bottom part. Since you are studying Geometry, he asks for your help.

Give the Geometric names of the solids that form the top and bottom parts. Then give the formula you will use to calculate the volume of each.

Farmer Hanson says the overall height from the ground to the top of the point is 51 feet. The top tapered part is 12 feet high, and the straight bottom part 39 feet high. The diameter of the bottom part is 36 feet which is also the diameter of the base of the top part. Using this information find the volume of the top part to the nearest tenth cubic foot showing your work. Use 3.1416 for pi or use the [π] button on your calculator.

Find the volume of the bottom part (show your work) then add your result from B above to find the total volume. State the total volume of the bin to the nearest cubic foot. Use 3.1416 for pi or use the [π] button on your calculator. Show your work.

Answer 1

Explanation:

The top part is a cone. It's volume is:

V = ⅓ π r² h

where r is the radius (half the diameter) and h is the height.

The bottom part is a cylinder. It's volume is:

V = π r² h

where r is the radius (half the diameter) and h is the height.

The radius of the cone is 36/2 = 18 ft, and the height is 12 ft. So the volume is:

V = ⅓ π (18 ft)² (12 ft)

V = 4,071.5 ft³

The radius of the cylinder is 36/2 = 18 ft, and the height is 39 ft. So the volume is:

V = π (18 ft)² (39 ft)

V = 39,697.2 ft³

Therefore, the total volume is:

4,071.5 ft³ + 39,697.2 ft³ ≈ 43,769 ft³