Advertisements
Advertisements
Question
A circular path has to be constructed around a circular lawn. If the outer and inner circumferences of the path are 88 cm and 44 cm respectively, find the width and area of the path
Advertisements
Solution
Outer circumference of the circular lawn = 88 cm
2πR = 88 cm
Inner circumference of the lawn 2πr = 44 cm
2πR – 2πr = 88 – 44
`2 xx 22/7 ("R" - "r")` = 44
(R – r) = `(44 xx 7)/(2 xx 22)`
Outer radius – Inner radius = 7 cm
∴ Width of the lawn = 7 cm
Also 2πR + 2πr = 88 + 44
2π(R + r) = 132
π(R + r) = `132/2`
= 66 cm
Area of the path = πR2 – πr2 sq.units
= π(R + r)(R – r)
= 66 × 7
Area of the path = 462 cm2
APPEARS IN
RELATED QUESTIONS
A school ground is in the shape of a circle with radius 103 m. Four tracks each of 3 m wide has to be constructed inside the ground for the purpose of track events. Find the cost of constructing the track at the rate of ₹ 50 per sq.m
The figure shown is the aerial view of the pathway. Find the area of the pathway
A rectangular garden has dimensions 11 m × 8 m. A path of 2 m wide has to be constructed along its sides. Find the area of the path
The formula to find the area of the circular path is
The formula to find the width of the circular path is
Four circles are drawn side by side in a line and enclosed by a rectangle as shown below. If the radius of each of the circles is 3 cm, then calculate:
(i) The area of the rectangle.
(ii) The area of each circle.
(iii) The shaded area inside the rectangle.
A cow is tethered with a rope of length 35 m at the centre of the rectangular field of length 76 m and breadth 60 m. Find the area of the land that the cow cannot graze?
A path 5 m wide runs along the inside of the rectangular field. The length of the rectangular field is three times the breadth of the field. If the area of the path is 500 m2 then find the length and breadth of the field
A circular path has to be constructed around a circular ground. If the areas of the outer and inner circles are 1386 m2 and 616 m2 respectively, find the width and area of the path
A goat is tethered with a rope of length 45 m at the centre of the circular grassland whose radius is 52 m. Find the area of the grassland that the goat cannot graze
