RD Chapter 15 Areas Related to Circles Ex 15.1 Solutions
Question - 21 : - The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr? [NCERT Exemplar]
Answer - 21 : -
Given,radius of wheel, r = 35 cm
Circumference of the wheel = 2πr
= 2 x (22/7) x35 = 220 cm
But speed of the wheel = 66 kmh-1
= (66x1000/60) m/mm
= 1100 x 100 cm min-1
= 110000 cm min-1
∴ Numberof revolutions in 1 min
= (110000/220)=500 revolution
Hence, required number of revolutions per minute is 500.
Question - 22 : - A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per m2. [NCERT Exemplar]
Answer - 22 : -
Given that, a circular pond is surrounded by a wide path.
The diameter of circular pond = 17.5 m
Question - 23 : - A circular park is surrounded by a rod 21 m wide. If the radius of the park is 105 m, find the area of the road. [NCERT Exemplar]
Answer - 23 : - Given that, a circular park is surrounded by a road.
Width of the road = 21 m
Radius of the park (r1)= 105 m
.’. Radius of whole circular portion (park + road),
re = 105 + 21 = 126m
Now, area of road = Area of whole circular portion – Area of circular park
= πr2 – πr2 [∵ area of circle = πr2]
Question - 24 : - A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square. [NCERT Exemplar]
Answer - 24 : - Let the side of a square be a and the radius of circle be r.
Given that, length of diagonal of square = 8 cm
Question - 25 : - A path of 4 m width runs round a semi¬circular grassy plot whose circumference is 81 (5/’7)m. Find:
(i) the area of the path
(ii) the cost of gravelling the path at the rate of ₹1.50 per square metre
(iii) the cost of turfing the plot at the rate of 45 paise per m2.
Answer - 25 : - Width of path around the semicircular grassy plot = 4 m
Circumference of the plot = 81 (5/7)m
= (572/7) m
Let r be the radius of the plot, then
Question - 26 : - Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.
Answer - 26 : -
Radius of first circle (r1) = 3.5 cm
Radius of second circle (r2) = 7 cm
Question - 27 : - A path of width 3.5 m runs around a semi¬circular grassy plot whose perimeter is 72 m. Find the area of the path. (Use π = 22/7) [CBSE 2015]
Answer - 27 : -
Perimeter of semicircle grassy plot = 72 m
Let r be the radius of the plot
Question - 28 : - A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14) [CBSE 2014]
Answer - 28 : -
Diameterof circular pond (d) = 17.5 m
Radius (r) =(1725/2) =8.75 m
Width of path = 2m
∴ Radius of outer cirlce (R) = 8.75 + 2 = 10.75 m
Area of path = (R2 – r2)π
= [(10.75)2 – (8.75)2](3.14)
= 3.14(10.75 + 8.75) (10.75 – 8.75)
= 3.14 x 19.5 x 2 = 122.46 m2
Cost of 1 m2 for constructingthe path ₹25 m2
∴ Total cost = ₹ 122.46 x 25 = ₹3061.50
Question - 29 : - The outer circumference of a circular race-track is 528 m. The track is every¬where 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre (Use π= 22/7).
Answer - 29 : -
Let R and r be the radii of the outer and inner of track.
Outer circumference of the race track = 528 m
Question - 30 : - A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
Answer - 30 : -
Width of the road = 7 m
Circumference of the park = 352 m
Let r be the radius, then 2πr = 352