Advertisements
Advertisements
Question
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
Advertisements
Solution
Radius of the ground R = 103 m
Width of a track W = 3 m
Width of 4 tracks = 4 × 3 = 12 m
Radius of the ground without track
r = (103 – 12) m
r = 91 m
Area of 4 tracks = Area of the ground – Area of the ground without track
= πR2 – πr2 sq.units
= π(R2 – r2) sq.units
= `22/7 [103^2 - 91^2]`
= `22/7 [103 + 91] [103- 91] "m"^2`
= `22/7 xx 194 xx 12`
= `51216/7`
= 7316.57 m2
∴ Area of 4 tracks = 7316.57 m2
Cost of constructing 7316.57 m2 = ₹ 50
∴ Cost of constructing 7316.57 m2 = ₹ 50 × 7316.57
= ₹ 3,65,828,57
Cost of constructing the track ₹ 3,65,828,57
APPEARS IN
RELATED QUESTIONS
There is a circular lawn of radius 28 m. A path of 7 m width is laid around the lawn. What will be the area of the path?
A circular carpet whose radius is 106 cm is laid on a circular hall of radius 120 cm. Find the area of the hall uncovered by the carpet
The figure shown is the aerial view of the pathway. Find the area of the pathway
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 area of the circular path is
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
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
