Answer :
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.
- 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.
