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Gabe made a rectangular sandbox for his brother to play in. Gabe wants to paint only the sides of the sandbox.

What is the surface area of the sides of the sandbox that Gabe wants to paint?

A. 27 ft²
B. 30 ft²
C. 47 ft²
D. 60 ft²

Sagot :

To determine the surface area of the sides of Gabe's rectangular sandbox that he wants to paint, we start by understanding the dimensions of the sandbox. Let's consider the following dimensions:

- Width: 3 feet
- Length: 5 feet
- Height: 2 feet

Here are the steps to find the surface area of the sides:

1. Calculate the perimeter of the base of the sandbox:
- The base of the sandbox is a rectangle, so its perimeter [tex]\(P\)[/tex] is given by:
[tex]\[ P = 2 \times (\text{width} + \text{length}) \][/tex]
- Substituting in the given dimensions:
[tex]\[ P = 2 \times (3 + 5) = 2 \times 8 = 16 \text{ feet} \][/tex]

2. Calculate the surface area of the sides of the sandbox:
- The surface area [tex]\(A\)[/tex] of just the sides can be calculated by multiplying the perimeter of the base by the height of the sandbox:
[tex]\[ A = P \times \text{height} \][/tex]
- Substituting the perimeter and height:
[tex]\[ A = 16 \times 2 = 32 \text{ square feet} \][/tex]

Given these calculations, the surface area of the sides of the sandbox that Gabe wants to paint is:
[tex]\[ \boxed{32 \text{ square feet}} \][/tex]

It appears the correct answer is not among the listed choices ([tex]\(27 \text{ ft}^2\)[/tex], [tex]\(30 \text{ ft}^2\)[/tex], [tex]\(47 \text{ ft}^2\)[/tex], [tex]\(60 \text{ ft}^2\)[/tex]). However, based on the calculations, the surface area of the sides is indeed 32 square feet.
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