Question

1. the box is shaped like a rectangular prism. the base of the box measures 8 feet by 10 feet. the total surface area of the box is 340 square feet. what is the height of the rectangular prism?

h= type your answer...

Explanation:

Step1: Recall surface area formula

The surface area \( S \) of a rectangular prism is given by \( S = 2(lw + lh + wh) \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 10 \) ft, \( w = 8 \) ft, and \( S = 340 \) sq ft.

Step2: Substitute known values

Substitute into the formula: \( 340 = 2(10\times8 + 10h + 8h) \)
Simplify inside the parentheses: \( 340 = 2(80 + 18h) \)

Step3: Divide both sides by 2

\( \frac{340}{2}=80 + 18h \)
\( 170 = 80 + 18h \)

Step4: Subtract 80 from both sides

\( 170 - 80 = 18h \)
\( 90 = 18h \)

Step5: Solve for h

Divide both sides by 18: \( h=\frac{90}{18}=5 \)

Answer:

5