Advertisements
Advertisements
Question
A piece of wire of length 108 cm is bent to form a semicircular arc bounded by its diameter. Find its radius and area enclosed.
Advertisements
Solution
Length of wire = 108 cm
Let r be the radius of the semicircle
πr+ 2r = 108
⇒ `r(pi + 2) = 108 ⇒ r(22/7 + 2) = 108`
⇒ `36/7 r = 108 ⇒ r = (108 xx 7)/36 = 21` cm
Area = `(pir^2)/2 = 22/(7 xx 2) xx 21 xx 21 = 1386/2` cm2
= 693 cm2
APPEARS IN
RELATED QUESTIONS
In the following figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:
the perimeter of the part ABEF.
Find the area of a shaded region in the the following figure,where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π = 22/7 and \[\sqrt{3}\] = 1.73)
The area of a circle is 220 cm2. The area of ta square inscribed in it is
If diameter of a circle is increased by 40%, then its area increase by
ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). The length of one of its diagonals is ______.
A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.
Find the areas of both the segments of a circle of radius 42 cm with central angle 120°. [Given, sin 120° = `sqrt(3)/2` and `sqrt(3) = 1.73`.]
The circumference of a circular table is 88 m. Find its area.
Find the area of the biggest circle that can be cut from a rectangular piece 44cm by 28cm. also, find the area of the paper left after cutting out the circle.
The floor of the circular swimming pool whose radius is 7 m has to be cemented at the rate of ₹ 18 per m2. Find the total cost of cementing the floor
