11 3/4 and 2 and 23 3/4 The triangular prism shown below represents a display case. Which of the following is the best estimate of the volume of the display case in cubic inches?
To find the volume of a triangular prism, we use the formula V = (1/2) * base * height * length.
Given that the base of the prism is 11 3/4, the height is 2, and the length is 23 3/4, we can substitute these values into the formula:
V = (1/2) * 11 3/4 * 2 * 23 3/4
First, convert all mixed numbers to improper fractions:
11 3/4 = 47/4
23 3/4 = 95/4
Now we can calculate the volume:
V = (1/2) * 47/4 * 2 * 95/4
V = (1/2) * 47/4 * 2 * 95/4
V = (1/2) * 47 * 2 * 95 / 16
V = 3,565 / 8
V = 445 5/8 cubic inches
Therefore, the best estimate of the volume of the display case is approximately 445 5/8 cubic inches.