Question

1. which of the rectangular prisms below has the greatest total surface area?

a
12 in 6 in 6 in
b
15 in 6 in 3 in

1. a shoe box is covered with packing paper before being shipped

Explanation:

Step1: Recall surface area formula

The total surface area of a rectangular prism is given by:
$$SA = 2(lw + lh + wh)$$
where $l$ = length, $w$ = width, $h$ = height.

Step2: Calculate SA for Prism A

Substitute $l=12$, $w=6$, $h=6$:

$$\begin{align*} SA_A &= 2[(12 \times 6) + (12 \times 6) + (6 \times 6)] \\ &= 2[72 + 72 + 36] \\ &= 2[180] \\ &= 360 \end{align*}$$

Step3: Calculate SA for Prism B

Substitute $l=15$, $w=6$, $h=3$:

$$\begin{align*} SA_B &= 2[(15 \times 6) + (15 \times 3) + (6 \times 3)] \\ &= 2[90 + 45 + 18] \\ &= 2[153] \\ &= 306 \end{align*}$$

Step4: Compare the two surface areas

$360 > 306$, so Prism A has a greater surface area.

Answer:

A. Rectangular prism with dimensions 12 in, 6 in, 6 in (surface area = 360 square inches)