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
Find the area of a circular pathway whose outer radius is 32 cm and inner radius is 18 cm.
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
A picture is painted on a ceiling of a marriage hall whose length and breadth are 18 m and 7 m respectively. There is a border of 10 cm along each of its sides. Find the area of the border
The formula to find the width of the circular path is
A path 2 m long and 1 m broad is constructed around a rectangular ground of dimensions 120 m and 90 m respectively. Find the area of the path
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 strip of 4 cm wide is cut and removed from all the sides of the rectangular cardboard with dimensions 30 cm × 20 cm. Find the area of the removed portion and area of the remaining cardboard
A rectangular field is of dimension 20 m × 15 m. Two paths run parallel to the sides of the rectangle through the centre of the field. The width of the longer path is 2 m and that of the shorter path is 1 m. Find (i) the area of the paths (ii) the area of the remaining portion of the field (iii) the cost of constructing the roads at the rate of ₹ 10 per sq.m
