AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The four circles have the same center and their radii are $4 cm, 5 cm, 6 cm$ and 7cm, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

10 : 12

9 : 13

13 : 5

3 : 9

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We have been given,
The four circles have the same center and their radii are

4 cm, 5 cm, 6 cm

and 7cm, respectively.
Question Image

We know that area of circle is

π \times r^{2}

, where

r

is radius.
Let

r_{1} = 4 cm, r_{2} = 5 cm, r_{3} = 6 cm, and r_{4} = 7 cm .

Area of small shaded ring is

π \times ({r_{2}}^{2} - {r_{1}}^{2})

\Rightarrow π \times (5^{2} - 4^{2})

\Rightarrow π \times 9 {cm}^{2}

Area of large shaded region is

π \times ({r_{4}}^{2} - {r_{3}}^{2})

\Rightarrow π \times (7^{2} - 6^{2})

\Rightarrow π \times 13 {cm}^{2}

The ratio of smaller to larger shaded regions is

\frac{Area of small shaded ring}{Area of large shaded region}

\Rightarrow \frac{π \times 9 {cm}^{2}}{π \times 13 {cm}^{2}}

\Rightarrow \frac{9}{13}

\Rightarrow 9 : 13

Therefore, the required ratio is 9:13.
Hence, option 2 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!