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The difference between the radius of two concentric circles is 14 cm and the difference between their areas is 1232 cm2. Find the radius of the smaller circle (using π as 22/7)
- a)6 cm
- b)7 cm
- c)9 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The difference between the radius of two concentric circles is 14 cm ...
There are two concentric circles.
Let the radius of the smaller circle be 'r' cm.
Then, the radius of the larger circle will be 'r + 14' cm.
Given: Difference between the areas of the circles = 1232 cm2
π (r + 14)2 – π (r)2 = 1232 cm2
π (r2 + 196 + 28r - r2) = 1232
392 = 28r + 196
196 = 28r
r = 196/28 = 7
Hence, the radius of the smaller circle is 7 cm.
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Community Answer
The difference between the radius of two concentric circles is 14 cm ...
Given information:
- The difference between the radius of two concentric circles is 14 cm.
- The difference between their areas is 1232 cm².
Let's assume:
- The radius of the larger circle is R cm.
- The radius of the smaller circle is (R - 14) cm.
Finding the difference in areas:
- The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
- The area of the larger circle is πR².
- The area of the smaller circle is π(R - 14)².
- The difference in areas is 1232 cm², so we can write the equation as:
πR² - π(R - 14)² = 1232
Simplifying the equation:
- Expanding the square term, we get:
πR² - π(R² - 28R + 196) = 1232
- Distributing the negative sign, we get:
πR² - πR² + 28πR - 196π = 1232
- Combining like terms, we get:
28πR - 196π = 1232
- Dividing both sides by 28π, we get:
R - 7 = 44
- Adding 7 to both sides, we get:
R = 51
Finding the radius of the smaller circle:
- We know that the radius of the smaller circle is (R - 14).
- Substituting the value of R, we get:
(51 - 14) = 37
Therefore, the radius of the smaller circle is 37 cm.
- The difference between the radius of two concentric circles is 14 cm.
- The difference between their areas is 1232 cm².
Let's assume:
- The radius of the larger circle is R cm.
- The radius of the smaller circle is (R - 14) cm.
Finding the difference in areas:
- The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
- The area of the larger circle is πR².
- The area of the smaller circle is π(R - 14)².
- The difference in areas is 1232 cm², so we can write the equation as:
πR² - π(R - 14)² = 1232
Simplifying the equation:
- Expanding the square term, we get:
πR² - π(R² - 28R + 196) = 1232
- Distributing the negative sign, we get:
πR² - πR² + 28πR - 196π = 1232
- Combining like terms, we get:
28πR - 196π = 1232
- Dividing both sides by 28π, we get:
R - 7 = 44
- Adding 7 to both sides, we get:
R = 51
Finding the radius of the smaller circle:
- We know that the radius of the smaller circle is (R - 14).
- Substituting the value of R, we get:
(51 - 14) = 37
Therefore, the radius of the smaller circle is 37 cm.
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