Mensuration Test 3

80 men took a dip in a tank of 60cm and 40cm. If the average displacement of water by a man is 60m³. Find the rise in water level?

 Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.

The weight of a cubic metre of a metal is 480 kg. It is melted and cast into a square rod whose length is 4 metres. A solid cube is taken out from one end of the rod. Find the weight of solid cube. 

The volume of a right circular  cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is?

The volume of a right circular cone is equal to the volume of a right circular cylinder that is 9 cm. high and whose diameter of base is 60 cm. The height of cone is 108 cm. Find the diameter of base of the cone. 

 A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct ? 

 A sphere of maximum volume is cut out from a solid hemisphere of radius r. Find the ratio of the volume of the hemisphere to that of the sphere?

The length and breadth of the floor of a room are 20 feet and 10 feet respectively. Square tiles of side 2 feet of three different colors are to be laid on the floor. White tiles are laid in the first row and all sides. If black tiles are laid in one third of the remaining and green tiles in the rest, how many green tiles will be there ?

A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm. are cut off at the corners and the remaining is folded to form an open rectangular box. The volume of the box is:

A rectangular water reservoir is 10.8 metres long and 3.75 metres wide at base. Water flows into it at the rate of 18m per sec. through the pipe having the cross section 7.5 cm × 4.5 cm. Find the height to which the water will rise in the reservoir in 30 minutes.