Advertisements
Advertisements
प्रश्न
The sum of diameter of two circles is 112 cm and the sum of their areas is 5236 cm2 Find the radii of the two circles.
उत्तर
Sum of the diameters = 112 cm
Therefore, sum of the radii = `112/2` cm = 56 cm
If r is the radius of one circle, radius of other circle is (56 - r)
Sum of the areas = π r2 + π (56 - r)2
⇒ π r2 + π (56 - r)2 = 5236
⇒ π r2 + π (3136 - 112 r + r2) = 5236
⇒ (r2 + 3136 - 112 r + r2) × `22/7` = 5236
⇒ 2r2 - 112r + 3136 = 1666
⇒ 2r2 - 112r + 3136 - 1666 = 0
⇒ 2r2 - 112r + 1470 = 0
⇒ r2 - 56r + 735 = 0
⇒ (r - 35)(r - 21) = 0
⇒ r = 35 , r = 21
Therefore, radii of the two circles is 35 cm and 21 cm
APPEARS IN
संबंधित प्रश्न
In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.
In the figure given below, PQRS is square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersections of its
diagonals. Find the total area of the two flower beds (shaded parts).
In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.
The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)
A doorway is decorated as shown in the figure. There are four semi-circles. BC, the diameter of the larger semi-circle is of length 84 cm. Centres of the three equal semicircles lie on BC. ABC is an isosceles triangle with AB = AC. If BO = OC, find the area of the shaded region. (Take `pi = 22/7`)
An arc of length 20𝜋 cm subtends an angle of 144° at centre of circle. Find the radius of the circle.
Find the angle subtended at the centre of circle of radius ‘a’ cm by an arc of length
`(api)/4` 𝑐𝑚
In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm,· then find the perimeter of the top of the table.
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3) "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.
The area of an equilateral triangle is `49sqrt(3)` cm2 . Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. [Take π = 1.73]
If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is
The circumference of a garden roller is 280 cm. How many revolutions does it make in moving 490 meters?
Find the area grazed by a horse tied with a 11. 2 m rope to a corner of a field measuring 25m by 15 m.
Each wheel of a car is of diameter 80 cm. How many completer revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?
The diameter of a circle is 5.6 cm. Find its circumference.
Find the circumference of the circles whose radii are given below.
49 cm
A race track is in the form of a circular ring whose outer and inner circumferences are 396 m and 352 m respectively. The width of the track is ____________.
The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of Rs 50 per metre.
A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.
