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Barbara wants a small round area rug for her bedroom. If the area of the rug has to be less than 50 square feet, what is the greatest diameter that the rug can be? Use 3.14 for pi.
(A) 6 feet
(B) 7 feet
(C) 7 feet

Barbara wants a small round area rug for her bedroom. If the area of the rug has to be less than $50$ square feet, what is the greatest diameter that the rug can be? Use $3$ . $14$ for $\pi$ . $\newline$ (A) $6$ feet $\newline$ (B) $7$ feet $\newline$ (C) $8$ feet

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Barbara wants a small round area rug for her bedroom. If the area of the rug has to be less than

50

square feet, what is the greatest diameter that the rug can be? Use

3

.

14

for

\pi

.

\newline

(A)

6

feet

\newline

(B)

7

feet

\newline

(C)

8

feet

Identify Formula: Identify the formula for the area of a circle, which is $A = \pi r^2$ , where $A$ is the area and $r$ is the radius of the circle.
Calculate Diameter: Understand that the diameter of the circle is twice the radius, so $D = 2r$ . We need to find the maximum diameter such that the area is less than $50$ square feet.
Set Up Inequality: Since we are given the area must be less than $50$ square feet, we set up the inequality \pi r^2 < 50.
Substitute Value: We are given the value of $\pi$ as $3.14$ , so we substitute this into the inequality to get 3.14r^2 < 50.
Isolate $r^2$ : Divide both sides of the inequality by $3.14$ to isolate $r^2$ on one side: r^2 < \frac{50}{3.14}.
Calculate Right Side: Calculate the right side of the inequality: $\frac{50}{3.14} \approx 15.9236$ .
Solve for r: Take the square root of both sides of the inequality to solve for r: r < \sqrt{15.9236}.
Calculate Maximum Radius: Calculate the square root of $15.9236$ to find the maximum radius: r < \sqrt{15.9236} \approx 3.99 feet.
Calculate Maximum Diameter: Since the diameter is twice the radius, we multiply the maximum radius by $2$ to find the maximum diameter: $D = 2 \times 3.99$ .
Find Whole Number Diameter: Calculate the maximum diameter: $D \approx 2 \times 3.99 \approx 7.98$ feet.
Find Whole Number Diameter: Calculate the maximum diameter: $D \approx 2 \times 3.99 \approx 7.98$ feet.Since the diameter must be a whole number that is available as an option and it must be less than $7.98$ feet, the greatest possible whole number diameter that is less than $7.98$ feet is $7$ feet.

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