Advertisements
Advertisements
Question
Find the area of the circle, length of whose circumference is equal to the sum of the lengths of the circumferences with radii 15 cm and 13 cm.
Advertisements
Solution
In a circle
Circumference = Sum of circumferences of two circle of radii 15 cm and 13 cm
Now circumference of first smaller circle = 2πr
= `2 xx 22/7 xx 15 = 660/7` cm
Circumference of the second smaller circle
= `2 xx 22/7 xx 13 = 572/7` cm
∴ Circumference of the bigger circle
= `660/7 + 572/7 = 1232/7` cm
Let R be its radius, then
`2pi"R" = 1232/7 ⇒ (2 xx 22)/7 "R" = 1232/7`
⇒ R = `1232/7 xx 7/44 = 28` cm
∴ Area of the circle = `pi"R"^2`
= `22/7 xx 28 xx 28 "cm"^2 = 2464` cm2
APPEARS IN
RELATED QUESTIONS
The base of an isosceles triangle measures 80 cm and its area is 2 `360 . cm^2` Find the perimeter of the triangle.
Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD 90° and ∠BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral.
Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB=90° and AC = 15 cm.
Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. (Use π = 22/7).
In the given figure, ABCD is a trapezium with AB || DC, AB = 18 cm DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then find the area of the shaded region.
(Use \[\pi = \frac{22}{7}\]
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
If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to `4/25"a"^2`.
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3)" cm"^2`. If the same wire is bent into the form of a circle, what will be the area of the circle?
The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km per hour.
The area of a circle is 154 cm2. Its diameter is ____________.
