Question

A prism has total surface area of 360 m² and volume of 60 m³. If the length, width, and height are doubled their original sizes, what will be the new volume? G.10B

Question 12 options:

360 m³


480 m³


120 m³


1,620 m³

Answer 1

To determine the new volume of the prism after doubling its dimensions, we can use the formula for the volume of a prism, which is given by:

\[
V = \text{base area} \times \text{height}
\]

When the length, width, and height of a prism are doubled, the volume will change as follows:

\[
\text{New Volume} = 2 \times \text{length} \times 2 \times \text{width} \times 2 \times \text{height} = 2^3 \times (\text{length} \times \text{width} \times \text{height}) = 8 \times \text{original volume}
\]

Given that the original volume of the prism is \(60 \, \text{m}^3\):

\[
\text{New Volume} = 8 \times 60 \, \text{m}^3 = 480 \, \text{m}^3
\]

Therefore, the new volume when the dimensions are doubled is \(480 \, \text{m}^3\).

The correct answer is:

**480 m³**