Kaylee found the surface area, in square inches, of a rectangular prism by using this formula:
[tex]$2(5 \times 3)+2(5 \times 8)+2(3 \times 8)$[/tex]
What is the surface area of the prism, in square inches?
Answer (2)
Calculate the product of 5 and 3, then multiply by 2: $2
\times (5
\times 3) = 30$.
Calculate the product of 5 and 8, then multiply by 2: $2
\times (5
\times 8) = 80$.
Calculate the product of 3 and 8, then multiply by 2: $2
\times (3
\times 8) = 48$.
Add the results to find the surface area: $30 + 80 + 48 =
\boxed{158}$.
Explanation
Analyze the problem and the given formula. The problem gives us a formula to calculate the surface area of a rectangular prism: $2(5
\times 3)+2(5
\times 8)+2(3
\times 8)$. Our goal is to find the numerical value of this expression, which represents the surface area in square inches.
Calculate the products inside the parentheses. Let's break down the calculation step by step:
First, we calculate the products inside the parentheses:
$5
\times 3 = 15$
$5
\times 8 = 40$
$3
\times 8 = 24$
Multiply each result by 2. Now, we multiply each of these results by 2:
$2
\times 15 = 30$
$2
\times 40 = 80$
$2
\times 24 = 48$
Add the results to find the surface area. Finally, we add these values together to find the total surface area:
30 + 80 + 48 = 158
State the final answer. Therefore, the surface area of the rectangular prism is 158 square inches.
Examples
Understanding surface area is crucial in many real-world applications. For example, when you're wrapping a gift, you need to know the surface area to determine how much wrapping paper you'll need. Similarly, when painting a room, knowing the surface area of the walls helps you calculate how much paint to buy. In manufacturing, calculating the surface area of objects is essential for determining the amount of coating needed to protect them from corrosion or wear. These calculations ensure efficiency and cost-effectiveness in various projects.
The surface area of the rectangular prism calculated using the formula is 158 square inches, achieved by breaking down the components of the formula and adding the results together.
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