Advertisements
Advertisements
Question
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm2. Find the length of the wire. If the same wire is bent to the largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
Advertisements
Solution
Area of the square made wire = 484 cm2
∴ Length (side) = `sqrt"Area"=sqrt484` = 22 cm
(i) Perimeter of wire = 4 × Side
= 4 × 22 = 88 cm
∴ Circumference of circular wire = 88 cm
∴ Radius (r) = `"C"/(2π)=(88xx7)/(2xx22)"cm"` = 14 cm
(ii) ∴ Area of the circle = πr2
= `22/7xx14xx14` = 616 cm2
APPEARS IN
RELATED QUESTIONS
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2 find the area of the lawn.
In the figure given below, find the area of shaded region: (All measurements are in cm)
The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.
Find the area of a triangle whose base is 30 cm and the height is 18 cm.
Find the area of an equilateral triangle whose each side is 16 cm. (Take `sqrt3`= 1.73)
Find the base of a triangle whose area is 360 cm2 and height is 24 cm.
The legs of a right-angled triangle are in the ratio 4 : 3 and its area is 4056 cm2. Find the length of its legs.
The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radius
(ii) diameters
(iii) circumference
A wire is along the boundary of a circle with a radius of 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.
From each corner of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.
