Q.1
Two cans have the same height equal to 21 cm. One can is cylindrical, the diameter of whose base is 10 cm. The other can has square base of side 10 cm. What is the difference in their capacities ?
Q.2
The radii of two sphere are in the ratio 3 : 2. Their volumes will be in the ratio :
Q.3
The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is :
Q.4
A cube of length 1 cm is taken out from a cube of length 8 cm. What is the weight of the remaining portion ?
Q.5
Capacity of a cylindrical vessel is 25.872 litres. If the height of the cylinder is three times the radius of its base, what is the area of the base ?
Q.6
The ratio of the volumes of a right circular cylinder and a sphere is 3 : 2. If the radius of the sphere is double the radius of the base of the cylinder, find the ratio of the total surface areas of the cylinder and the sphere :
Q.7
If the radius of a sphere is increased by 10%, then the volume will be increased by :
Q.8
A metallic cone of radius 12 cm and height 24 cm is ,melted and made into spheres of radius 2 cm each. How many spheres are there ?
Q.9
A hemispherical bowl has 3.5 cm radius. It is to be painted inside as well as outside. The cost of painting it at the rate of Rs. 5 per 10 sq. cm will be :
Q.10
If the radii of two spheres are in the ratio 1 : 4, then their surface areas are in the ratio :
Q.11
What part of a ditch, 48 metres long, 16.5 metres board and 4 metres deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 metres and length 56 metres ?
Q.12
If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, then the curved surface area of the cone is :
Q.13
A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm so that the level may be raised 20 cm in 5 hours ?
Q.14
Each side of a cube measures 8 metres. What is the volume of the cube ?
Q.15
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is :
Q.16
How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m × 6 m × 22.5 cm ?
Q.17
A solid cube just gets completely immersed in water when a 0.2 kg mass is placed on it. If the mass is removed, the cube is 2 cm above the water level. What is the length of each side of the cube ?
Q.18
The radius of base and curved surface area of a right cylinder is 'r' units and 4πrh square units respectively. The height of the cylinder is :
Q.19
A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is :
Q.20
The ratio of the volume of a cube to that of a sphere which will fit inside the cube is :
Q.21
A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal everywhere is 0.4 cm thick. The volume of the metal is :
Q.22
A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wood wasted is :
Q.23
Ice cream completely filled in a cylinder of diameter 35 cm and height 32 cm is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served this way is :
Q.24
The volume of a cuboid is twice that of a cube . If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, the total surface area of the cube is :
Q.25
The volume of a right circular cylinder, 14 cm in height is equal to that of a cube whose edge is 11 cm. The radius of the base of the cylinder is :
Q.26
If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio if their radii is :
Q.27
A school room is be built to accommodate 70 children so as to allow 2.2 m2 of floor and 11 m3 of space for each child. If the room be 14 metres long, what must be its breadth and height ?
Q.28
A rectangular water tank is open at the top. Its capacity is 24 m3. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the inner and outer surface of the tank at the rate of Rs. 10 per m2 is :
Q.29
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
Q.30
A solid metallic right circular cylinder of base diameter 16 m and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. Find the curved surface area of the cone. [Use $$\pi $$ = 3.14]
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