3D Mensuration test 4

1.A tank 40 m long, 30 m broad and 12 m deep is dug in a field 1000 m long and 30 m wide. By how much will the level of the field rise if the earth dug out of the tank is evenly spread over the field ?

2.A sphere is cut into two hemispheres. One of them is used as bowl. It takes 8 bowlfuls of this to fill a conical vessel of height 12 cm and radius 6 cm. The radius of the sphere(in centimetre) will be

3.A hollow sphere of internal and external diameter 6 cm and 10 cm respectively is melted into a right circular cone of diameter 8 cm. The height of the cone is

4.A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

5.A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl is

6.If the volume of a sphere is numerically equal to its surface area then its diameter is;

7.5 persons live in a tent. If each person requires 16 m² of floor area and 100 m³ space for air then the height of the cone of smallest size to accomodate these persons would be?

8.If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to

9.The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is:

10.The volume (in m3 ) of rain water that can be collected from 1.5 hectares of ground in a rainfall of 5 cm is

11.A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour, How much water ( in-litres) will fall into sea in a minute ?

12.Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2m. In how much time will the cistern be filled ?

13.Water flows at the rate of 10 metres per minute from cylindrcial pipe 5 mm in diameter, How long it will take to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm?

144.A plate of square base made of brass is of length x cm and thickness 1 mm.The plate weighs 4725 gm. If 1 cubic cm of brass weighs 8.4 gram, then the value of x is:

15.The diameter of a 120 cm long roller is 84 cm. It takes 500 complete revolutions of the roller to level a ground. The cost of levelling the ground at Rs. 1.50 sq. m. is:

16.The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2 . The volume of the cuboid is :

17.The volume of two spheres are in the ratio 8 : 27. The ratio of their surface area is:

18.The base radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is :

19.The ratio of the volume of two cones is 2 : 3 and the ratio of radii of their base is 1 : 2. The ratio of their height is

20.If the height of a given cone be doubled and radius of the base remains the same the ratio of the volume of the given cone to that of the second cone will be