48.0k views
1 vote
Which of the following quantities could be represented by the product of 14, 22, and 32?

a) The volume of a rectangular prism with a length of 7 units, a width of 11 units, and a height of 16 units.
b) The area of a rectangular prism with a length of 7 units, a width of 11 units, and a height of 16 units.
c) The volume of a rectangular prism with a length of 14 units, a width of 22 units, and a height of 32 units.
d) The area of a rectangular prism with a length of 14 units, a width of 22 units, and a height of 32 units.

1 Answer

0 votes

Final answer:

The product of 14, 22, and 32 represents the volume of a rectangular prism with those dimensions; thus, option (c) is correct as it corresponds to calculating volume, which is length × width × height.

Step-by-step explanation:

The product of 14, 22, and 32 can be interpreted in terms of the volume of a rectangular prism. In mathematics, the volume of a rectangular prism is found by multiplying its length by its width and by its height. Therefore, option (c) is correct - the volume of a rectangular prism with a length of 14 units, a width of 22 units, and a height of 32 units could be represented by the product of these numbers. This is because volume is a measure of how much space an object occupies and is expressed in cubic units.

Calculating the volume of a rectangular prism can be done step-by-step as follows:

  1. Multiply the length, the width, and the height together: 14 × 22 × 32.
  2. The product gives the volume in cubic units, hence this would give 14 × 22 × 32 cubic units.

Options (a), (b), and (d) are incorrect; (a) has different dimensions so the product would not be the same, (b) is incorrect because area cannot have a height component, and (d) which concerns surface area includes a different calculation involving the sum of the areas of all the sides of the prism, not the product of its dimensions.

User Puetzk
by
7.3k points