Advertisements
Advertisements
Question
A 7m wide road surrounds a circular garden whose area is 5544m2. Find the area of the road and the cost of tarring it at the rate of Rs.150 per m2.
Advertisements
Solution
we know,
The area of the ring between two concentric circles equals the area of the larger circle minus the area of smaller circle.
Let the radius of the outer and inner ring be R and r respectively.
Here the circular garden is the inner circle and the 7m wide road os the ring area of the ring between two concentric circles = π(R2 - r2)
The Area of a Circle with radius r = πr2
Here,
πr2 = 5544m2
⇒ r = 42
⇒ R = 42 + 7
= 49
inner Circle has radius r
= 42 and outer Circle has radius R
= 49
π(492 - 422)
= `(22)/(7) xx (2401 - 1764)`
= `(22)/(7) xx 637`
= 2002m2
The cost of paying the road at the rate of Rs.150per m2
= 2002 x 150
= Rs.3,00,300.
APPEARS IN
RELATED QUESTIONS
A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)
In the following figure, the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find
- the length of the boundary.
- the area of the shaded region.
In the following figure, ABC is a right angled triangle in which ∠A = 90°, AB = 21 cm and AC = 28 cm. Semi-circles are described on AB, BC and AC as diameters. Find the area of the shaded region.
What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?
If the difference between the circumference and radius of a circle is 37 cm, then using π = \[\frac{22}{7}\] the circumference (in cm) of the circle is
In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10, find the area of the shaded region.
Two circles touch each other externally. The sum of their areas is 74π cm2 and the distance between their centers is 12 cm. Find the diameters of the circle.
The diameter of a wheel is 0.70 m. Find the distance covered by it in 500 revolutions. If the wheel takes 5 minutes to make 500 revolutions; find its speed in :
(i) m/s
(ii) km/hr.
Lalitha wants to buy a round carpet of radius is 63 cm for her hall. Find the area that will be covered by the carpet
The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is ______.
