Advertisements
Advertisements
प्रश्न
A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m2.
Advertisements
उत्तर
There are two concentric semi circles. The diameter of the inner circle = 42 or radius, a = 21m. The radius of the outer circle, b = 21 + 7 = 28m.
Because the radius of a Circle with diameter d is r = `"d"/(2)`
The Area of the inner Semi-circle with radius a = `(pi"a"^2)/(2) = (pi21^2)/(2)`
∴ The Area of the outer Semi-circle with radius b = `(pi"b"^2)/(2) = (pi28^2)/(2)`
and The Area of a Semi-circle with radius r = `(pi"r"^2)/(2)`
The Area of the flower bed
= `(pi28^2)/(2) - (pi21^2)/(2)`
= `pi/(2)(28^2 - 21^2)`
= `pi/(2)(784 - 441)`
= `pi/(2)(343)`
= `(22)/(7 xx 2)(343)`
= 539m2.
APPEARS IN
संबंधित प्रश्न
In the following figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
In the following figure, there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate:
(i) the area of the shaded region
(ii) the cost of painting the shaded region at the rate of 25 paise per cm2 , to the nearest rupee.
In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:
the height of the tunnel
In the following figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park.
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m2 . Find the cost of ploughing the field. [Take `π =22/7`].
Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.
Area of circle of radius ‘n’ units is
On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
