() at a farm, animals are fed bales of hay and buckets of gain. each bale of hay is in the shape of a rectangular prism. the base side lengths 2 feet and 3 feet, and the height is 5 feet. each bucket of grain is a cylinder with diameter of 3 feet. the height of the bucket is 5 feet as the height of bale. a. which is larger in area, the rectangular base of the bale 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

A. Circular base of the bucket

B. Bucket

Step-by-step explanation:

We are given that,

1. The dimensions of the rectangular prism are,

Length = 2 feet, Width = 3 feet and Height = 5 feet.

So, we have,

Area of the rectangular base =

i.e. Area of the rectangular base =

i.e. Area of the rectangular base = 6 feet²

Also, we have,

Volume of the prism =

i.e. Volume of the prism =

i.e. Volume of the prism = 30 feet³

2. The dimensions of the cylinder are given as,

Diameter = 3 feet i.e Radius = = 1.5 feet

Height = 5 feet

Then, we have,

Area of the circular base =

i.e. Area of the circular base =

i.e. Area of the circular base =

i.e. Area of the circular base = 7.07 feet²

Also, we have,

Volume of the cylinder =

i.e. Volume of the cylinder =

i.e. Volume of the cylinder =

i.e. Volume of the cylinder =

i.e. Volume of the cylinder = 35.34 feet³

PART A: Since we have,

Area of the rectangular base = 6 feet² < 7.07 feet² = Area of the circular base

Hence, the circular base of the bucket is larger in area.

PART B: We have,

Volume of the prism = 30 feet³ < 35.34 feet³ = Volume of the cylinder

Hence, the bucket is larger in volume.

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step-by-step explanation: