Advertisements
Advertisements
प्रश्न
Two circles touch each other externally. The sum of their areas is 74π cm2 and the distance between their centers is 12 cm. Find the diameters of the circle.
Advertisements
उत्तर
Let the radius of the circles be r1 and r2.
So, r1 + r2 = 12 ⇒ r2 = 12 - r1
Sum of the areas of the circles = 74π
⇒ πr12 + πr12 = 74π
⇒ r12 + r12 = 74
⇒ r12 + ( 12 - r1 )2 = 74
⇒ r12 + 144 - 24r1 + r12 = 74
⇒ 2r12 - 24r1 + 70 = 0
⇒ r12 - 12r1 + 35 = 0
⇒ ( r1 - 7 )( r1 - 5 ) = 0
⇒ r1 = 7 or r1 = 5
Ir r1 = 7 cm, then r2 = 5 cm
If r1 = 5 cm, then r2 = 7 cm
So, the diameters of the circles will 10 cm and 14 cm.
APPEARS IN
संबंधित प्रश्न
The outer circumference of a circular race-track is 528 m . The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre.
`(use pi=22/7). `
How many revolutions a circular wheel of radius r metres makes in covering a distance of s metres?
If the circumference and the area of a circle are numerically equal, then diameter of the circle is
From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semicircular portion with BC as diameter is cut off. Find the area of the remaining paper.
A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m. If the length of the rope is 7 m, find the area of the field which the horse cannot graze. Write the answer correct to 2 places of decimal.
In the given figure, ∆ABC is right-angled at A. Find the area of the shaded region if AB = 6 cm, BC = 10 cm and O is the centre of the incircle of ∆ABC.
The diameter of a wheel is 0.70 m. Find the distance covered by it in 500 revolutions. If the wheel takes 5 minutes to make 500 revolutions; find its speed in :
(i) m/s
(ii) km/hr.
Find the area of the dining table whose diameter is 105 cm
The formula used to find the area of the circle is ________ sq.units
What is the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40cm and 9cm?
