Question
A pillow box with a height of 1/2 inches needs to have a volume greater than 2 in what is the solution of an inequality describing the possible area of the base b A b > 1 1/2 inches B b > 2 1/2 inches C b > 1 inches D B > 4 inches
Answers
GPT-4o mini
To solve the problem, we need to find the area of the base \( b \) of a pillow box with a given height such that the volume exceeds 2 cubic inches.
The volume \( V \) of a box can be calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
In this case, the volume \( V \) must be greater than 2 cubic inches, and the height \( h \) is \( \frac{1}{2} \) inches. Therefore, we can write the inequality as follows:
\[
b \cdot \frac{1}{2} > 2
\]
Now, we can multiply both sides of the inequality by 2 to eliminate the fraction:
\[
b > 4
\]
Thus, the solution to the inequality describing the possible area of the base \( b \) is:
\[
b > 4 \text{ inches}
\]
The correct option is **D**: \( b > 4 \) inches.
The volume \( V \) of a box can be calculated using the formula:
\[
V = \text{Base Area} \times \text{Height}
\]
In this case, the volume \( V \) must be greater than 2 cubic inches, and the height \( h \) is \( \frac{1}{2} \) inches. Therefore, we can write the inequality as follows:
\[
b \cdot \frac{1}{2} > 2
\]
Now, we can multiply both sides of the inequality by 2 to eliminate the fraction:
\[
b > 4
\]
Thus, the solution to the inequality describing the possible area of the base \( b \) is:
\[
b > 4 \text{ inches}
\]
The correct option is **D**: \( b > 4 \) inches.