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The volume of a rectangular prism is 30 cm³. The length of the prism is doubled, the width is tripled,

and the height is divided by four. The volume of the new prism is
(A) 31 cm³
(B) 120 cm³
(C) 60 cm³
(D) 45 cm³

User Wendu
by
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1 Answer

7 votes

Answer:

(D) 45 cm^3

Explanation:

The formula for the volume of a rectangular prism is given by:

V = LWH, where

  • V is the volume in units cubed,
  • L is the length,
  • W is the width,
  • and H is the height.

Since the prism's original volume is 30 cm³, we have:

Original Volume = L W H = 30 cm³

Since the length is doubled, the width is tripled, and the height is divided by four, the formula for the new volume is given by:

New Volume = (2L)(3W)(H/4)

Now we can simplify the expression:

New Volume = 2 × 3 × (L × W × H / 4)

New Volume = 6 × (L × W × H / 4)

New Volume = (6 / 4) × (L × W × H)

New Volume = (3 / 2) × (L × W × H)

  • Thus, the original volume changes by a factor of 3/2.

Thus, we can find the New Volume using the formula:

New Volume = (3 / 2) × 30 cm³

New Volume = 45 cm³

Therefore, the volume of the new prism is 45 cm³, so the correct answer is D.

User Josephoneill
by
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