Answer:
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 = [tex]Length\times Width[/tex]
i.e. Area of the rectangular base = [tex]2\times 3[/tex]
i.e. Area of the rectangular base = 6 feet²
Also, we have,
Volume of the prism = [tex]whl[/tex]
i.e. Volume of the prism = [tex]3\times 5\times 2[/tex]
i.e. Volume of the prism = 30 feet³
2. The dimensions of the cylinder are given as,
Diameter = 3 feet i.e Radius = [tex]\frac{3}{2}[/tex] = 1.5 feet
Height = 5 feet
Then, we have,
Area of the circular base = [tex]\pi r^2[/tex]
i.e. Area of the circular base = [tex]\pi (1.5)^2[/tex]
i.e. Area of the circular base = [tex]2.25\pi[/tex]
i.e. Area of the circular base = 7.07 feet²
Also, we have,
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
i.e. Volume of the cylinder = [tex]\pi (1.5)^{2}\times 5[/tex]
i.e. Volume of the cylinder = [tex]\pi 2.25\times 5[/tex]
i.e. Volume of the cylinder = [tex]11.25\pi[/tex]
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.
