Question

At a farm animals are fed bales of hay nad buckets of grain. Each bale of hay is in the shape of a rectangular prism the bas each bucket of grain is a cylinder with a diameter of 3 fee the height of the bucket is 5 feet the same as the height of the bale has side lenghts 2 feet and 3 feet and the height of 5 feet.

a.Which is larger in area,the rectangular base or the circular base of the bucket?Explain how you know

B.which is larger in volume,the bale or the bucket?Explain how you know.

Answer 1

Answer: a. The area of the rectangular base of the bale of hay is 2 feet * 3 feet = 6 square feet.

The area of the circular base of the bucket is π * (diameter/2)^2, where the diameter is 3 feet, so the area is π * (3/2)^2 = π * (9/4) = 9π/4 square feet.

Since π is approximately equal to 3.14, the area of the circular base is approximately 9 * 3.14 / 4 = 6.935 square feet, which is less than the area of the rectangular base.

So the rectangular base of the bale of hay is larger in area.

b. The volume of the bale of hay is 2 feet * 3 feet * 5 feet = 30 cubic feet.

The volume of the bucket is π * (diameter/2)^2 * height, where the diameter is 3 feet and the height is 5 feet, so the volume is π * (3/2)^2 * 5 = π * (9/4) * 5 = 45π/4 cubic feet.

Since π is approximately equal to 3.14, the volume of the bucket is approximately 45 * 3.14 / 4 = 34.65 cubic feet, which is less than the volume of the bale of hay.

So the bale of hay is larger in volume.

Explanation: