Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Two stars each of one solar mass (= 2×1030 kg) are approaching each other for a
head on collision. When they are a distance 109
km, their speeds are negligible.
What is the speed with which they collide ? The radius of each star is 104
km.
Assume the stars to remain undistorted until they collide. (Use the known value
of G).
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
A satellite orbits the earth at a height of 400 km above the surface. How much
energy must be expended to rocket the satellite out of the earth’s gravitational
influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of
the earth = 6.4 × 106
m; G = 6.67 × 10–11 N m2 kg–2
.
In Figure. ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.
A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m2
Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60° (Use π = 3.14).
Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.
The diameters of front and rear wheels of a tractor are 80 cm and 2 m respec- tively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.
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