Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)
A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹ 60 per metre.
A regular hexagon is inscribed in a circle. If the area of hexagon is \[24\sqrt{3}\] , find the area of the circle. (Use π = 3.14)
If three circles of radius a each, are drawn such that each touches the other two, prove that the area included between them is equal to `4/25"a"^2`.
A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP ⊥ CD, HQ ⊥ FI and EL ⊥ DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure.
The area of a sector of a circle with radius r, making an angle of x° at the centre is
If the radius of a circle is doubled, its area becomes ____________.
It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be ______.
A table cover of dimensions 3 m 25 cm × 2 m 30 cm is spread on a table. If 30 cm of the table cover is hanging all around the table, find the area of the table cover which is hanging outside the top of the table. Also find the cost of polishing the table top at ₹ 16 per square metre.
Read the following passage:
People of a circular village Dharamkot want to construct a road nearest to it. The road cannot pass through the village. But the people want the road at a shortest distance from the centre of the village. Suppose the road starts from A which is outside the circular village (as shown in the figure) and touch the boundary of the circular village at B such that AB = 20 m. Also the distance of the point A from the centre O of the village is 25 m. |
Based on the above information, answer the following questions:
- If B is the mid-point of AC, then find the distance AC.
- Find the shortest distance of the road from the centre of the village.
- Find the circumference of the village.
OR
Find the area of the village.
