Q51 A cylindrical bucket, 42 cm high and 28 cm of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 28 cm, find the slant height of the heap.

Q52 A solid cuboid of iron with dimensions 23 cm x 20 cm x 25 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 7 cm and 5 cm respectively. Find the length of pipe.

Q53 A spherical ball of radius 5 cm is melted and recast into three spherical balls. The radii of two of the balls are 3.5 cm and 2 cm. Find the diameter of the third ball.

Q54 Rain water, which falls on a flat rectangular surface of length 10 m and breadth 5 m is transfered into a cylindrical vessel of internal radius 10 cm .What will be the height(m) of water in the cylindrical vessel if rainfall of 2 cm has fallen?

Q55 The difference between the sides at right angles in a right- angled triangle is 5 cm, with hypotenuse 9cm. Find its perimeter.

Q56 A room 4.2 m long and 2.8 m broad is covered with carpet, leaving an uncovered margin of 15 cm all around the room. If the breadth of the carpet is 40 cm, find its cost at Rs.100 per metre.

Q57 A 70 m by 54 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at Rs.50 per sq.m.

Q58 The cost of painting the four walls of a room 20 m high at Rs.15 per sq.m is Rs.7500 and the cost of covering the floor with mat at Rs.50 per sq.m is Rs.1500. Find the length of the room.

Q59 A spherical glass vessel has a cylindrical neck 5 cm long, 4 cm in diameter, and the diameter of the spherical part is 8 cm. Finds its volume.

Q60 A metallic solid right circular cone 30 cm high and whose vertical angle is $60°$
is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter $\frac{1}{20}$
cm, find the length of the wire(km).