Advertisements
Advertisements
Question
The areas of two circles are in the ratio 49 : 64. Find the ratio of their circumferences.
Advertisements
Solution
Given, the area of two circles are in the ratio 49 : 64
Area of a circle = πr2
Let area of the first circle = `pir_1^2`
And area of the second circle = `pir_2^2`
According to the question,
`49/64 = (pir_1^2)/(pir_2^2)`
⇒ `49/64 = r_1^2/r_2^2`
⇒ `(7)^2/(8)^2 = r_1^2/r_2^2`
⇒ `(7/8)^2 = (r_1/r_2)^2`
∴ r1 = 7 and r2 = 8
The ratio of circumferences of these two circles
= `(2pir_1)/(2pir_2)` ...[∵ Circumference of circle = 2πr]
= `r_1/r_2`
= `7/8`
Hence, required ratio is 7 : 8
APPEARS IN
RELATED QUESTIONS
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
Find the area of a trapezium whose parallel sides of lengths 10 cm and 15 cm are at a distance of 6 cm from each other. Calculate this area as
the sum of the areas of two triangles and one rectangle.
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
If the area of a trapezium is 28 cm2 and one of its parallel sides is 6 cm, find the other parallel side if its altitude is 4 cm.
The two parallel sides and the distance between them are in the ratio 3: 4: 2. If the area of the trapezium is 175 cm2, find its height.
In a trapezium if the sum of the parallel sides is 10 cm and the area is 140 sq.cm, then the height is
When the non-parallel sides of a trapezium are equal then it is known as
A ground is in the form of isosceles trapezium with parallel sides measuring 42 m and 36 m long. The distance between the parallel sides is 30 m. Find the cost of levelling it at the rate of ₹ 135 per sq.m
The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.
Find the area of the following fields. All dimensions are in metres.
