60.5k views
5 votes
A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.

How much taller is the large prism than the small prism?
Write your answer as a whole number or decimal. Do not round.

User Manifest
by
8.0k points

1 Answer

2 votes

Answer:

The large prism is 5 inches taller than the small prism

Explanation:

We know that the formula for volume of a rectangular prism is

V = lwh, where

  • V is the volume in cubic units
  • l is the length,
  • w is the width,
  • and h is the height

Step 1: We're given the volume, length, and width for both rectangular prisms, but not the height. We can find the height of each rectangular prism by rewriting the volume formula in terms of h (i.e., isolate h), which gives us:

V / (lw) = h

Step 2: To find the height of the small prism, we plug in 100 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

100 / (5 * 4) = h

100 / 20 = h

5 inches = height

Optional Confirmation of Step 2:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 100 for V, 5 for l, and 4 for w;

100 = 5 * 4 * 5

100 = 20 * 5

100 = 100

Step 3: To find the height of the large prism, we plug in 200 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

200 / (5 * 4) = h

200 / 20 = h

10 inches = height

Optional Confirmation of Step 3:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 200 for V, 5 for l, and 4 for w;

200 = 5 * 4 * 10

200 = 20 * 10

200 = 200

Step 5:

  • We now know that the heights of the small and large prism are 5 inches and 10 inches respectively
  • We subtract the small prism's height (5 inches) from the large prism's height (10 inches)
  • This will show how much taller is the large prism than the small prism:

10 - 5 = 5 inches taller

User Achyut Pokhrel
by
9.2k points

No related questions found