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Sub 505 Level|   Geometry|      
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Bunuel
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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 10:07
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If two identical circles of diameter 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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B
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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 10:49
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Bunuel
If two identical circles of radius 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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Sir the image is Missing. Kindly insert one for inference.
Thank You

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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 10:54
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Bunuel
If two identical circles of radius 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

Are You Up For the Challenge: 700 Level Questions

Sir the image is Missing. Kindly insert one for inference.
Thank You

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Added the image. Thank you.
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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 11:11
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Bunuel

If two identical circles of radius 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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Sir I tried solving using every single method but I am getting 450π as the area of shaded region. Given the radius of smaller circle is 15. The area of one smaller circle is 225π and 2 will have 450π
Area of bigger circle is 900π since diameter of smaller circle is radius for bigger circle.
Kindly check through the options.

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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 11:17
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yashikaaggarwal
Bunuel

If two identical circles of radius 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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Sir I tried solving using every single method but I am getting 450π as the area of shaded region. Given the radius of smaller circle is 15. The area of one smaller circle is 225π and 2 will have 450π
Area of bigger circle is 900π since diameter of smaller circle is radius for bigger circle.
Kindly check through the options.

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Should have been diameter instead of radius. Fixed.
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If two identical circles of diameter 15 cm are tangent to each other Updated on: 06 May 2020, 11:25
Originally posted by Vij2019 on 06 May 2020, 11:18.
Last edited by Vij2019 on 06 May 2020, 11:25, edited 1 time in total.
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Based on updated information, answer should be B:
1. Diameter of two smaller circles is 15cm and thereby their combined area which is the unshaded region is: 2*π*(15/2)^2 = 225/2 cm^2.
2. Radius of bigger circle is same as the diameter of the smaller circle: 15cm
3. Area of larger circle: π*15^2 = 225π cm^2.
4. Area of shaded region = Area of larger circle - Area of two smaller circles
= 225π - 225/2π which gives us 225/2 cm^2
which is 112.5π cm^2 .


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If two identical circles of diameter 15 cm are tangent to each other 06 May 2020, 11:24
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Answer is B
Radius of bigger circle = diameter of smaller circle = 15
πr^2 = π*15*15 = 225π -----(1)
Area of smaller circles = 2π(7.5)^2 = 112.5π -----(2)
Subtracting 2 from 1 we get 112.5
OA is B

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If two identical circles of diameter 15 cm are tangent to each other 07 May 2020, 08:26
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Bunuel

If two identical circles of diameter 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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diameter of larger circle = 30 ; radius 15
area large circle ; 15^2*pi ; 225pi
and of two smaller circle the radius ; 7.5^2 *2 * pi ; 112.5pi
shaded area ; 225pi-112.5pi ; 112.5pi
OPTION B
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If two identical circles of diameter 15 cm are tangent to each other 07 May 2020, 08:31
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Bunuel

If two identical circles of diameter 15 cm are tangent to each other at the center of the larger circle as shown above, what is the area of the shaded region?

A. 56.25π cm^2
B. 112.5π cm^2
C. 225π cm^2
D. 275π cm^2
E. 337.4π cm^2

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Radius of the smaller (Unshaded Circles ) = 15/2

So, Area of 2 Unshaded Circles is 2*π*15/2*15/2 = 112.5π

Radius of the Bigger circle is 15 So, Area of the bigger Circle is 15^2*π = 225π

Thus, Area of the unshaded circle is 225π - 112.5π = 112.5π , Answer must be (B)
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