Question
A sandbox in the shape of a rectangular prism is 12ft.
high and needs to contain at least 42 ft.3
of sand. How would you write an inequality to express the possible area of the base, b
, of the sandbox? You will find the option to add inequality symbols in the Comparison (<)
keyboard.(1 point)
42
12b
high and needs to contain at least 42 ft.3
of sand. How would you write an inequality to express the possible area of the base, b
, of the sandbox? You will find the option to add inequality symbols in the Comparison (<)
keyboard.(1 point)
42
12b
Answers
GPT-4o mini
To express the relationship between the volume of the sandbox and the area of the base, we can start with the formula for the volume of a rectangular prism:
\[
\text{Volume} = \text{Area of the base} \times \text{Height}
\]
In this case, the volume must be at least 42 cubic feet, and the height is 12 feet. If we let \( b \) represent the area of the base of the sandbox, we can set up the inequality as follows:
\[
12b \geq 42
\]
To isolate \( b \), we can divide both sides of the inequality by 12:
\[
b \geq \frac{42}{12}
\]
Simplifying \(\frac{42}{12}\) gives:
\[
b \geq 3.5
\]
Thus, the inequality expressing the possible area of the base \( b \) of the sandbox is:
\[
b \geq 3.5
\]
So, the original inequality in the context of your question would be:
\[
12b \geq 42
\]
\[
\text{Volume} = \text{Area of the base} \times \text{Height}
\]
In this case, the volume must be at least 42 cubic feet, and the height is 12 feet. If we let \( b \) represent the area of the base of the sandbox, we can set up the inequality as follows:
\[
12b \geq 42
\]
To isolate \( b \), we can divide both sides of the inequality by 12:
\[
b \geq \frac{42}{12}
\]
Simplifying \(\frac{42}{12}\) gives:
\[
b \geq 3.5
\]
Thus, the inequality expressing the possible area of the base \( b \) of the sandbox is:
\[
b \geq 3.5
\]
So, the original inequality in the context of your question would be:
\[
12b \geq 42
\]