Advertisements
Advertisements
Question
The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13.2 cm. Find the radii of the two circles.
Advertisements
Solution
Let r1 and r2 be the radii of two circles.
⇒ r1 + r2 = 10.5 ....(i)
And,
`2π"r"_(6.3-4.21) - 2π"r"_2` = 13.2
⇒ `2 xx (22)/(7) xx ("r"_1 - "r"_2)` = 13.2
⇒ r1 - r2 = `(13.2 xx 7)/(2 xx 22)`
⇒ r1 - r2 = 2.1 ....(ii)
Adding (i) and (ii), we get
2r1 = 12.6
⇒ r1 = 6.3cm
Now,
r1 - r2 = 2.1
⇒ 6.3 - r2 = 2.1
⇒ r2 = 4.2cm.
APPEARS IN
RELATED QUESTIONS
A rectangular park 358 m long and 18 m wide is to be covered with grass, leaving 2.5 m uncovered all around it. Find the area to be laid with grass.
In the given figure ABCD is quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 12 cm. Calculate the area of the quadrilateral.
Find the area of a parallelogram with base equal to 25 cm and the corresponding height measuring 16.8 cm.
A chord of a circle of radius 20 cm sub tends an angle of 900 at the centre . Find the area of the corresponding major segment of the circle
( Use \[\pi = 3 . 14\])
If the perimeter of a semi-circular protractor is 36 cm, then its diameter is
If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is
The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to the sum of the areas of the two given circles.
The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm2, find the area of the bigger circle.
Pizza factory has come out with two kinds of pizzas. A square pizza of side 45 cm costs ₹ 150 and a circular pizza of diameter 50 cm costs ₹ 160 (see figure). Which pizza is a better deal?
Read the following passage:
People of a circular village Dharamkot want to construct a road nearest to it. The road cannot pass through the village. But the people want the road at a shortest distance from the centre of the village. Suppose the road starts from A which is outside the circular village (as shown in the figure) and touch the boundary of the circular village at B such that AB = 20 m. Also the distance of the point A from the centre O of the village is 25 m. |
Based on the above information, answer the following questions:
- If B is the mid-point of AC, then find the distance AC.
- Find the shortest distance of the road from the centre of the village.
- Find the circumference of the village.
OR
Find the area of the village.
