A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6
The OA is C.
We know that,
$$Area_{circle}=\pi r^2=\pi\cdot10^2\approx314$$
$$Area_{square}=24^2=576$$
$$\frac{Area_{circle}}{Area_{square}}=\frac{314}{576}=\frac{157}{288}$$
Now this fraction is obviously between 1/2 and 3/4, then
$$\frac{1}{2}=\frac{144}{288}$$
and
$$\frac{3}{4}=\frac{216}{288}$$
157 is closer to 144 than to 216. Hence C is the correct option.
A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6
The OA is C.
We know that,
$$Area_{circle}=\pi r^2=\pi\cdot10^2\approx314$$
$$Area_{square}=24^2=576$$
$$\frac{Area_{circle}}{Area_{square}}=\frac{314}{576}=\frac{157}{288}$$
Now this fraction is obviously between 1/2 and 3/4, then
$$\frac{1}{2}=\frac{144}{288}$$
and
$$\frac{3}{4}=\frac{216}{288}$$
157 is closer to 144 than to 216. Hence C is the correct option.
