Advertisements
Advertisements
Question
A circular field of radius 105 m has a circular path of uniform width of 5 m along and inside its boundary. Find the area of the path.
Advertisements
Solution
The radius of circular field, `r_1 = 105`m
Width of path = 50 m
∴ The radius of the inner circle, `r_2 = 105 - 5 = 100`m
Area of path = `pir_1^2 - pir_2^2`
= `22/7[(105)^2 - (100)^2]`
= `22/7(105 + 100)(105 - 100)`
= `22/7 xx 205 xx 5`
= `22550/7`m2
= `3221 3/7`m2
APPEARS IN
RELATED QUESTIONS
A rectangular plot measures 125 m by 78 m. It has a 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 m2.
A carpet is laid on the floor of a room 8 m by 5 m. There is a border of constant width all around the carpet. If the area of the border is 12 m2, find its width.
In Figure 5, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR =12 cm. Find the lengths of QM, RN and PL ?
What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?
The length of an arc of a circle, subtending an angle of 54° at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.
In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use `sqrt(3) = 1.73` and π = 3.14.]
On increasing the diameter of a circle by 40%, its area will be increased by ______.
If the radius of a circle is doubled, its area becomes ____________.
If the radius of a circle is tripled, the area becomes ______.
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.
