Question

if the width of the rectangular prism is doubled, which of the following is true? the volume is half as large. the surface area is half as large. the volume is twice as large. the surface area is twice as large.

Explanation:

Step1: Recall Volume Formula

Volume of rectangular prism: \( V = l \times w \times h \)
Original: \( l = 2 \), \( w = 4 \), \( h = 3 \) (assuming units, values from diagram)
Original \( V = 2 \times 4 \times 3 = 24 \)

Step2: Double the Width

New width \( w' = 2 \times 4 = 8 \)
New volume \( V' = 2 \times 8 \times 3 = 48 \)

Step3: Compare Volumes

\( V' = 2 \times V \) (since \( 48 = 2 \times 24 \))

Check Surface Area (optional, but to rule out others):
Original SA: \( 2(lw + lh + wh) = 2(2×4 + 2×3 + 4×3) = 2(8 + 6 + 12) = 52 \)
New SA: \( 2(2×8 + 2×3 + 8×3) = 2(16 + 6 + 24) = 2×46 = 92 \), not double of 52. So volume doubles, surface area doesn't.

Answer:

The volume is twice as large.