Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35 m wide. If the area of the path is 420 m2, find the width of the path.
The area of a square filed is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?
In the following figure, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.
If a wire is bent into the shape of a square, then the area of the square is 81 cm2. When wire is bent into a semi-circular shape, then the area of the semi-circle will be ______.
The radius of a circle is 20 cm. It is divided into four parts of equal area by drawing three concentric circles inside it. Then, the radius of the largest of three concentric circles drawn is
Area of the largest triangle that can be inscribed in a semi-circle of radius r units is ______.
The given figures show a rectangle ABCD inscribed in a circle as shown alongside.
If AB = 28 cm and BC = 21 cm, find the area of the shaded portion of the given figure.
The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8.30 a.m. and 9.05 a.m.
On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Find the diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm.
