Q.1
How many lead shots each 3 mm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm ?
Q.2
A metallic sphere of radius 5 cm is melted to make a cone with base of the same radius. What is the height of the cone ?
Q.3
Except for one face of a given cube, identical cubes are glued through their faces to all the other faces of the given cube. If each side of the given cube measures 3 cm, then what is the total surface area of the solid body thus formed ?
Q.4
The length of the longest rod that can be placed in a room of dimensions 10 m × 10 m × 5 m is :
Q.5
The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672 m2, what is the volume of the cylinder ?
Q.6
The height of a closed cylinder of given volume and the minimum surface area is :
Q.7
The number of circular pipes with an inside diameter of 1 inch which will carry the same amount of water as a pipe with an inside diameter of 6 inches is :
Q.8
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is :
Q.9
If the diameter of a sphere is 6 m, its hemisphere will have a volume of :
Q.10
A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is :
Q.11
Base of a right prism is a rectangle, the ratio of whose length and breadth is 3 : 2. If the height of the prism is 12 cm and total surface area is 288 sq.cm the volume of the prism is :
Q.12
Given that 1 cu. cm of marble weights 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is :
Q.13
An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimension 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is :
Q.14
Water is poured into an empty cylindrical tank at a constant rate for 5 minutes. After the water has been poured into the tank. the depth of the water is 7 feet. The radius of the tank is 100 feet. Which of the following is the best approximation for the rate at which the water was poured into the tank ?
Q.15
The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is :
Q.16
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is :
Q.17
The radius of the base and height of a metallic solid cylinder are r cm and 6 cm respectively. It is melted and recast into a solid cone of the same radius of base. The height of the cone is :
Q.18
V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :
(i) V1 + V2 + 2V3 < V4
(ii) V1 + 4V2 + V3 < V4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
Q.19
The curved surface area of a sphere is 5544 sq.cm. Its volume is :
Q.20
A hemispherical bowl of internal radius 12 cm contains liquid. This liquid is to be filled into cylindrical container of diameter 4 cm and height 3 cm. The number of containers that is necessary to empty the bowl is :
Q.21
A cistern, open at the top, is to be lined with sheet of lead which weights 27 kg/m2. The cistern is 4.5 m long and 3 m wide and holds 50 m3. The weight of lead required is :
Q.22
Length of each edge of a regular tetrahedron is 1 cm. It volume is :
Q.23
The base of a right prism is a trapezium whose lengths of two parallels sides are 10 cm and 6 cm and distance between them is 5 cm. If the heights of the prism is 8 cm, its volume is :
Q.24
A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and breadth of the reservoir is 3.5 m, then the depth of the reservoir will be :
Q.25
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200% respectively. Then the increase in the volume of the cuboid is :
Q.26
A water tank is 30 m long, 20 m wide and 12 m deep. It is made of iron sheet which is 3 m wide. The tank is open at the top. If the cost of the iron sheet is Rs. 10 per metre, then the total cost of the iron sheet required to build the tank is :
Q.27
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes ?
Q.28
What is the weight of water contained in a conical vessel 21 cm deep and 16 cm in diameter ?
Q.29
If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube ?
Q.30
By what percent the volume of a cube increases if the length of each edge was increased by 50%
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