A smaller circle is inscribed in a larger circle shown as above figure

Question

7.11.png A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through the center of the larger circle, what is the ratio of the area of the region shaded to the area of the larger circle? A. \frac{1}{2} B. \frac{2}{3} C. \frac{3}{4} D. \frac{4}{5} E. \frac{5}{6}

chetan2u · Answer

Hi,

The figure is incorrect and does not represent a sketch that is intended by Q.

Also there can be various smaller circles that can satisfy the Q so the Q must be meaning :- 
 smaller circle passing through the centre and touching the circumference at just one point.

Solution:-
This circle will have the DIAMETER equal to the RADIUS of larger circle...
Area of larger circle =πr^2...
Area of smaller circle= π(\frac{r}{2)}^2=π\frac{r^2}{4} ..
Thus area of shaded region = πr^2-π\frac{r^2}{4}=\frac{3πr^2}{4} ...
Thus ratio =3/4

C

Adityagmatclub · Answer

How diameter of small circle equals to radius of larger circle??

generis · Answer

chetan2u , thanks for clarifying. I thought the same, but waited for an expert . . . Adityagmatclub , see my figure and solution immediately below where smaller circle passes through center of larger circle and smaller circle touches larger circle's circumference at just one point. circle--in-circle.png Similar to chetan2u 's analysis: Disregard the figure. Rely instead on the phrase "is inscribed in," see my figure above, where the smaller circle is completely inside the larger circle, which is what I understand "inscribed" to mean. Smaller circle passes through larger circle's center and touches larger circle's circumference at just one point. Shaded area = Area of large circle - area of smaller circle. Let radius of larger circle be 4. Radius of larger circle is diameter of small circle, and d = 2r, so radius of small circle is: d = 4 = 2r means r = 2. Area of large circle = \pi*r^2 = \pi*4^2 = 16 \pi Area of small circle (r is 2) = 4 \pi Large - small = 16 \pi - 4 \pi = 12 \pi --> is the area of the shaded portion Ratio of area of shaded portion to area of larger circle is \frac{12\pi}{16\pi} = \frac{3}{4} Answer C Hope it helps.

cbh · Answer

Good catch, I was also confused after reading and only by assuming that was able to resolve the case

MathRevolution · Answer

==> Square of the ratio of the length=ratio of the area. The diameter of the smaller circle is equal to the radius of the larger circle, so the ratio of the length becomes 1:2. Then, the ratio of the area becomes 1^2:2^2=1:4. Thus, if the area of the smaller circle=k, the area of the larger circle=4k. Therefore, the area of the region shaded:the area of the larger circle=(4k-k):4k=3:4=¾.

The answer is C.
Answer: C

The answer is C.
Answer: C

pushkarajnjadhav · Answer

Please correct the figure, I got it wrong just because of faulty figure.

Jimbo1912 · Answer

This question is a complete waste of time with current attachment

Posted from my mobile device

bumpbot · Answer

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A smaller circle is inscribed in a larger circle shown as above figure

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A smaller circle is inscribed in a larger circle shown as above figure

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