Question

a bagel shop sells coffee in a container shaped like a rectangular prism. a graphic designer who works for the bagel shop drew the net below to create a design for the container.
diagram with 24 cm, 10 cm, 17 cm
note: figure is not drawn to scale.
what is the surface area of the container?
a. 1,636 sq cm
b. 219 sq cm
c. 818 sq cm
d. 1,228 sq cm

Explanation:

Step1: Recall surface area formula for rectangular prism

The surface area \( SA \) of a rectangular prism is given by \( SA = 2(lw + lh + wh) \), where \( l \) is length, \( w \) is width, and \( h \) is height. From the net, we can identify \( l = 24 \) cm, \( w = 17 \) cm, \( h = 10 \) cm.

Step2: Calculate each pair of faces

First, calculate \( lw \): \( 24\times17 = 408 \)
Then, calculate \( lh \): \( 24\times10 = 240 \)
Next, calculate \( wh \): \( 17\times10 = 170 \)

Step3: Substitute into surface area formula

Substitute these values into \( SA = 2(lw + lh + wh) \):
\( SA = 2(408 + 240 + 170) \)
First, add the terms inside the parentheses: \( 408 + 240 + 170 = 818 \)
Then, multiply by 2: \( 2\times818 = 1636 \)

Answer:

A. 1,636 sq cm