Question

A manufacturer wants to produce a 4"× 2"× 5" rectangular box to hold teabags using the net shown. Study the box and the net. Then complete the statements below to find the surface area of the box.

Answer 1

It is 40 because I multiply

Answer 2

The surface area of the rectangular box is
`\( \boxed{76 \, \text{in}^2} \).`

Step-by-step explanation:

The surface area of a rectangular box is the sum of the areas of its six faces. In this case, we have three pairs of opposite faces with equal dimensions. The dimensions of the box are given as 4"×2"×5". Each pair of opposite faces contributes twice to the total surface area. Therefore, the surface area (\(A_{\text{total}}\)) can be calculated using the formula:

`\[ A_{\text{total}} = 2(lw + lh + wh) \]`

Substituting the given values, where
`\( l \) is the length, \( w \)`is the width, and \( h \) is the height:

`\[ A_{\text{total}} = 2(4 * 2 + 4 * 5 + 2 * 5) \]`

Simplifying this expression gives us the final answer. The units for the surface area are square inches
`(\( \text{in}^2 \)).` Therefore, the calculated surface area for the given rectangular box is
`\( \boxed{76 \, \text{in}^2} \).`

In conclusion, understanding the geometry of the box and utilizing the surface area formula allows us to determine the total surface area efficiently. The final result,
`\(76 \, \text{in}^2\), r`epresents the amount of material needed to manufacture the rectangular box to hold teabags.