Question

Thomas has two containers, a rectangular prism and a cylinder, as shown below.Answer BOTH questions. A) Which of the containers has a greater volume? Explain your answer in words or by showing your work. Include units in your answer.B) Which of the containers has a greater surface area? Explain your answer in words or by showing your work. Include units in your answer.

Answer 1

Part A

Volume of the rectangular prism = 240 cm³

Volume of a cylinder = 352 cm³

The cylinder has a greater volume.

Surface Area of the rectangular prism = 268 cm²

Surface Area of the cylinder = 276.57cm²

The cylinder also has a greater surface area.

Step-by-step explanation

Part A

Volume of a rectangular prism = LBH

L = Length of the rectangular prism = 10 cm

B = Breadth of the rectangular prism = 8 cm

H Height of the rectangular prism = 3 cm

Volume = (10)(8)(3) = 240 cm³

Volume of a cylinder = πR²H

R = Radius of the cylinder = (Diameter/2) = (8/2) = 4 cm

H Height of the cylinder = 7 cm

π = pi = (22/7)

Volume of a cylinder = πR²H = π (4²) (7) = 352 cm³

The cylinder has a greater volume.

Part B

Surface Area of a rectangular prism = 2 (LB + LH + BH)

L = Length of the rectangular prism = 10 cm

B = Breadth of the rectangular prism = 8 cm

H Height of the rectangular prism = 3 cm

Surface Area of the rectangular prism = 2 (LB + LH + BH)

Surface Area of the rectangular prism = 2 (10×8 + 10×3 + 8×3)

Surface Area of the rectangular prism = 2 (80 + 30 + 24) = 268 cm²

Surface area of a cylinder = 2πR² + 2πRH

R = Radius of the cylinder = (Diameter/2) = (8/2) = 4 cm

H Height of the cylinder = 7 cm

Surface Area of the cylinder = 2π(4²) + 2π(4)(7) = 32π + 56π = 88π = 276.57cm²

The cylinder also has a greater surface area.

Hope this Helps!!!