Question

kendalls dad is building her a toy box that is a rectangular prism. he wants to determine how much paint to buy to cover the outside of the toy box.

given the dimensions of the toy box, determine the surface area.

hint: use the formula sheet to determine the formula(s) needed to solve the problem.

a. \\(1,382\text{ in}^2\\)
b. \\(2,111\text{ in}^2\\)
c. \\(17,220\text{ in}^2\\)
d. \\(4,202\text{ in}^2\\)

Explanation:

⚡ Using what you learned: surface area of prisms, pyramids, cylinders, cones, spheres

Step 1: Identify the dimensions

The toy box is a rectangular prism with the following dimensions:

• Length \( (l) = 41\text{ in.} \)
• Width \( (w) = 20\text{ in.} \)
• Height \( (h) = 21\text{ in.} \)

Step 2: Apply the surface area formula

The formula for the total surface area (\(SA\)) of a rectangular prism is:

$$ SA = 2(lw + lh + wh) $$

Substitute the given values into the formula:

$$ SA = 2((41 \times 20) + (41 \times 21) + (20 \times 21)) $$

Step 3: Calculate the area of each pair of faces

Calculate the products inside the parentheses:

• \( 41 \times 20 = 820 \)
• \( 41 \times 21 = 861 \)
• \( 20 \times 21 = 420 \)

Sum these values:

$$ 820 + 861 + 420 = 2,101 $$

Step 4: Multiply by 2 to find the total surface area

$$ SA = 2 \times 2,101 = 4,202\text{ in.}^2 $$

This matches option D.

Answer:

D (4,202 in.²)