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.

$a = 10 , b = 12$
A)46%
B)42%
C)10%
D)21%
E)58%

Question

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 = 12

$a = 10 , b = 12$
A)46% 
B)42% 
C)10% 
D)21% 
E)58%

Quizplus · Accepted Answer

The area of the rectangular room is $10 	imes 12 = 120$ 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: $$\frac{16\pi}{120} 	imes 100 \approx 42\%$$ Rounded to the nearest integer, the answer is $\boxed{	extbf{(B) }42\%}$.

The Floor of a Rectangular Room That Measures 10 Feet a=10,b=12a = 10 , b = 12a=10,b=12

The Floor of a Rectangular Room That Measures 10 Feet $a = 10 , b = 12$