A cardboard cereal box is $9\,\text{in.}$ by $2.5\,\text{in.}$ by $10\,\text{in.}$ What is the minimum amount of cardboard needed to create this cereal box? $\newline$ $A) \$275\,\text{in.}^2$ $\newline$ $B) \$230\,\text{in.}^2$ $\newline$ $C) \$225\,\text{in.}^2$ $\newline$ $D) \$180\,\text{in.}^2$

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Q. A cardboard cereal box is

9\,\text{in.}

2.5\,\text{in.}

10\,\text{in.}

What is the minimum amount of cardboard needed to create this cereal box?

\newline

A) \$275\,\text{in.}^2

\newline

B) \$230\,\text{in.}^2

\newline

C) \$225\,\text{in.}^2

\newline

D) \$180\,\text{in.}^2

Calculate Surface Area: To find the minimum amount of cardboard needed, we need to calculate the surface area of the box. A box has $6$ sides: $2$ of each are identical. The sides are as follows: two that are $9\text{in}$ by $2.5\text{in}$ , two that are $9\text{in}$ by $10\text{in}$ , and two that are $2.5\text{in}$ by $10\text{in}$ .
First Pair Calculation: Calculate the area of the first pair of sides: $9\,\text{in}$ by $2.5\,\text{in}$ . $\newline$ Area $= \text{length} \times \text{width} = 9\,\text{in} \times 2.5\,\text{in} = 22.5\,\text{in}^2$ . $\newline$ Since there are two of these sides, multiply by $2$ : $2 \times 22.5\,\text{in}^2 = 45\,\text{in}^2$ .
Second Pair Calculation: Calculate the area of the second pair of sides: $9\,\text{in}$ by $10\,\text{in}$ . $\newline$ Area $= \text{length} \times \text{width} = 9\,\text{in} \times 10\,\text{in} = 90\,\text{in}^2$ . $\newline$ Since there are two of these sides, multiply by $2$ : $2 \times 90\,\text{in}^2 = 180\,\text{in}^2$ .
Third Pair Calculation: Calculate the area of the third pair of sides: $2.5\,\text{in}$ by $10\,\text{in}$ . $\newline$ Area $= \text{length} \times \text{width} = 2.5\,\text{in} \times 10\,\text{in} = 25\,\text{in}^2$ . $\newline$ Since there are two of these sides, multiply by $2$ : $2 \times 25\,\text{in}^2 = 50\,\text{in}^2$ .
Total Surface Area Calculation: Add the areas of all three pairs of sides to get the total surface area of the box. $\newline$ Total surface area = $45\text{in}^2 + 180\text{in}^2 + 50\text{in}^2 = 275\text{in}^2$ .