Advertisements
Advertisements
प्रश्न
A wire in the form of a circle of radius 42cm. It is bent into a square. Determine the side of the square and compare the area of the regions enclosed in the two cases.
Advertisements
उत्तर
Let the side of the square = s and the radius of the circle = r
The Circumference of a circle with radius r = 2πr
The Circumference of a Circle with radius 42
= 2π x 42
= 264cm
The Area of a Circle with radius r
= πr2
= π(42)2
= 5544cm2
The Circumference of the Circle
= Perimeter of the square
⇒ Perimeter of the Square = 264cm
⇒ 4s = 264cm
⇒ s = 66cm
Area of a Square with side s = 4s2
Area of a Square with side 66
= 4(66)2
= 4356cm2
Ratio of Area of the Circle to the Area of the Square
= 5544:4356
= 14:11.
APPEARS IN
संबंधित प्रश्न
In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.
Below fig shows a sector of a circle, centre O. containing an angle 𝜃°. Prove that Perimeter of shaded region is 𝑟 (tan 𝜃 + sec 𝜃 +`(pitheta)/180`− 1)
The perimeter of a rhombus is 60 cm. If one of its diagonal us 18 cm long, find
(i) the length of the other diagonal, and
(ii) the area of the rhombus.
Choose the correct alternative answer for the following question.
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3) "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.
The wheels of the locomotive of a train are 2.1 m in radius. They make 75 revolutions in one minute.
The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is
Find the curved surface area , the total surface area and the volume of a cone if its :
Height = 16 cm , diameter = 24 cm
A metal wire, when bent in the form of an equilateral triangle of largest area, encloses an area of 484 `sqrt3` cm2. If the same wire is bent into the form of a circle of largest area, find the area of this circle.
Ratio of the circumference of a circle to its diameter is denoted by symbol ______.
