Asked by Nathan Papke on Jun 05, 2024
Verified
The floor of a rectangular room that measures 10 feet by 12 feet is partially covered with a circular rug with a radius of 4 feet (see figure) . What percent of the floor is covered by the rug? Round your answer to the nearest integer.
a=10,b=12a = 10 , b = 12a=10,b=12
A) 46%
B) 42%
C) 10%
D) 21%
E) 58%
Rectangular Room
A prism-shaped space with four walls at right angles to each other, typically used to describe a standard room shape.
Circular Rug
A rug in the shape of a circle, often used as a decorative piece in homes.
Radius
The measurement from the middle of a circle to a point on its outer boundary.
- Utilize geometric principles to address challenges associated with the perimeter, area, and congruent triangles.
- Address issues related to proportions within different settings, such as geometric situations and practical life examples.
Verified Answer
AL
Andre LewisJun 11, 2024
Final Answer :
B
Explanation :
The area of the rectangular room is $10 \times 12 = 120$ square feet. The area of the circular rug is $\pi(4^2) = 16\pi$ square feet. To find the percentage of the floor covered by the rug, we divide the area of the rug by the area of the floor and multiply by 100: 16π120×100≈42%\frac{16\pi}{120} \times 100 \approx 42\%12016π×100≈42% Rounded to the nearest integer, the answer is $\boxed{\textbf{(B) }42\%}$.
Learning Objectives
- Utilize geometric principles to address challenges associated with the perimeter, area, and congruent triangles.
- Address issues related to proportions within different settings, such as geometric situations and practical life examples.
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