Question

The volume of this rectangular prism is 19.8 cubic meters. The length of the prism is 2.5 meters and the width is 3.2 meters. What is the value of the height, d?

(A) 2.4 meters
(B) 2.7 meters
(C) 3.0 meters
(D) 3.3 meters

Answer 1

The height, d, of the rectangular prism with a volume of 19.8 cubic meters, length of 2.5 meters, and width of 3.2 meters is closest to 2.7 meters. We find this by dividing the volume by the product of the length and width.

Step-by-step explanation:

To find the value of the height, d, of the rectangular prism with a given volume of 19.8 cubic meters, length of 2.5 meters, and width of 3.2 meters, we use the formula for the volume of a prism: Volume = Length × Width × Height. Given the volume (V), length (l), and width (w), we can rearrange the formula to solve for the height (d): Height = Volume /(Length × Width).

First, multiply the length and width to find the base area:
Base Area = 2.5 m × 3.2 m = 8.0 m².

Then, divide the given volume by the base area to find the height:
Height = 19.8 m³ / 8.0 m² = 2.475 m.

The closest value to 2.475 meters among the given options is (B) 2.7 meters, which can be rounded up from 2.475 meters.