Section C Section C Checkpoint

Problem 1

Find the volume of each figure. Explain or show your reasoning.

a.
Rectangular prism with 1 extra row attached. Prism, 4 cubes by 3 cubes by 2 cubes. Extra row of 4 cubes attached to the side with 4 cubes.

b.
6-sided prism.
6-sided prism. Straight sides. All side lengths meet at right angles. Side lengths. Bottom, unlabeled length. Right side rises 6 inches, then goes left 8 inches, goes up 2 inches, then goes left 6 inches, then goes down an unlabeled length. Width shown as 4 inches.

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Solution

Sample responses:

  1. 28 cubic units. Sample response: I cut this figure into a 2-unit-by-3-unit-by-4-unit rectangular prism that has a volume of 24 cubic units, and there are 4 more cubes, so that's 28 cubic units. 

  2. 384 cubic inches. Sample response: I can cut this figure into two rectangular prisms. One prism has side lengths 8 inches by 6 inches by 4 inches and the other prism is 6 inches by 8 inches by 4 inches. Each has a volume of 8× 6× 48 \times 6 \times 4 or 192 cubic inches. The total volume is 384 cubic inches.

Show Sample Response
Sample Response

Sample responses:

  1. 28 cubic units. Sample response: I cut this figure into a 2-unit-by-3-unit-by-4-unit rectangular prism that has a volume of 24 cubic units, and there are 4 more cubes, so that's 28 cubic units. 

  2. 384 cubic inches. Sample response: I can cut this figure into two rectangular prisms. One prism has side lengths 8 inches by 6 inches by 4 inches and the other prism is 6 inches by 8 inches by 4 inches. Each has a volume of 8× 6× 48 \times 6 \times 4 or 192 cubic inches. The total volume is 384 cubic inches.

Problem 2

A jewelry box is shaped like a rectangular prism. The base of the box has an area of 200 square centimeters and its height is 6 centimeters. What is the volume of the jewelry box? Explain or show your reasoning.

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Solution

1,200 cubic centimeters. Sample response: I multiplied the area of the base by the height, 200×6=1,200200 \times 6 = 1,200.

Show Sample Response
Sample Response

1,200 cubic centimeters. Sample response: I multiplied the area of the base by the height, 200×6=1,200200 \times 6 = 1,200.