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Answer :
To find the width of the compost box, let's break down the problem step-by-step.
1. Understand the Volume Equation: The volume of the compost box is given as 6,930 cubic inches. The box is shaped like a rectangular prism, and the formula for the volume [tex]\( V \)[/tex] of a rectangular prism is:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
2. Substitute Known Values: We know that the length of the box is 40 inches, and both the width and the height of the box are the same, so let's call them both [tex]\( w \)[/tex].
[tex]\[
6,930 = 40 \times w \times w
\][/tex]
This simplifies to:
[tex]\[
6,930 = 40w^2
\][/tex]
3. Solve for [tex]\( w \)[/tex]: To find [tex]\( w \)[/tex], we first need to isolate [tex]\( w^2 \)[/tex] by dividing both sides of the equation by 40:
[tex]\[
w^2 = \frac{6,930}{40}
\][/tex]
4. Calculate [tex]\( w^2 \)[/tex]:
[tex]\[
w^2 = 173.25
\][/tex]
5. Find [tex]\( w \)[/tex]: To solve for [tex]\( w \)[/tex], take the square root of both sides:
[tex]\[
w = \sqrt{173.25}
\][/tex]
6. Round the Result: After solving the equation, we find that:
[tex]\[
w \approx 13.2
\][/tex]
Therefore, the width of the compost box is approximately 13.2 inches.
1. Understand the Volume Equation: The volume of the compost box is given as 6,930 cubic inches. The box is shaped like a rectangular prism, and the formula for the volume [tex]\( V \)[/tex] of a rectangular prism is:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
2. Substitute Known Values: We know that the length of the box is 40 inches, and both the width and the height of the box are the same, so let's call them both [tex]\( w \)[/tex].
[tex]\[
6,930 = 40 \times w \times w
\][/tex]
This simplifies to:
[tex]\[
6,930 = 40w^2
\][/tex]
3. Solve for [tex]\( w \)[/tex]: To find [tex]\( w \)[/tex], we first need to isolate [tex]\( w^2 \)[/tex] by dividing both sides of the equation by 40:
[tex]\[
w^2 = \frac{6,930}{40}
\][/tex]
4. Calculate [tex]\( w^2 \)[/tex]:
[tex]\[
w^2 = 173.25
\][/tex]
5. Find [tex]\( w \)[/tex]: To solve for [tex]\( w \)[/tex], take the square root of both sides:
[tex]\[
w = \sqrt{173.25}
\][/tex]
6. Round the Result: After solving the equation, we find that:
[tex]\[
w \approx 13.2
\][/tex]
Therefore, the width of the compost box is approximately 13.2 inches.
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