Advertisements
Advertisements
प्रश्न
A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.
Advertisements
उत्तर
The largest area of the circle is possible when,
diameter = 42
Therefore, radius = `42/2` = 21 cm
Therefore, Area of circle = π × (21)2
= 1386
Area of the rectangle = 55 × 42 = 2310 cm2
Therefore, area of remaining cardboard-
`= 42 xx 55 - pi (21)^2`
`= 42 xx 55 - 22/7 (21)^2`
= 2310 - 1386
= 924
Hence, the volume of the circle and area remaining cardboard-
= 1386 : 924
= 231 : 154
= 3 : 2
APPEARS IN
संबंधित प्रश्न
One side of a rectangle is 12 cm long and its diagonal measure 37 cm. Find the other side and the area of the rectangle.
In the following figure, PQRS is a square of side 4 cm. Find the area of the shaded square.
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 the following figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.
In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
The area of the circle that can be inscribed in a square of side 10 cm is
A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of the pendulum.
If a square in inscribed in a circle, find the ratio of the areas of the circle and the square.
Find the radius and circumference of a circle, whose area is :
(i) 154 cm2
(ii) 6.16 m2
Find the area enclosed between two concentric circles, If their radii are 6cm and 13cm respectively.
