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
A rectangular plot measure 125 m by 78 m. It has gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at` ₹ 75 per m^2`
A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m . Find the area of the path .
`("Use" pi= 22/7) `
Find the area of the following figure, in square cm, correct to one place of decimal. (Take π = 22/7).
In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.
Write the area of the sector of a circle whose radius is r and length of the arc is l.
If the diameter of a semi-circular protractor is 14 cm, then find its perimeter.
In the given figure, PQRS represents a flower bed. If OP = 21 m and OR = 14 m, find the area of the flower bed.
The area of the circle is 154 cm2. The radius of the circle is ______.
Find the area of the shaded region:
What is the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40cm and 9cm?
