Q.1
A cuboidal water tank contains 216 litres of water. Its depth is $$\frac{1}{3}$$ of its length and breadth is $$\frac{1}{2}$$ of $$\frac{1}{3}$$ of the difference between length and depth. The length of the tank is :
Q.2
A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood :
Q.3
The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base ?
Q.4
If the radius of the base and height of a cylinder and cone are each equal to r, and the radius of a hemisphere is also equal to r, then the volumes of the cone, cylinder and hemisphere are in the ratio ?
Q.5
A swimming bath is 24 m long and 15 m broad. When a number of men dive into the bath, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu.m, how many men are there in the bath ?
Q.6
If the volume of a sphere is divided by its surface area, the result is 27 cm. The radius of the sphere is :
Q.7
A sphere and a cube have equal surface area. The ratio of the volume of the sphere to that of the cube is :
Q.8
Find the cost of a cylinder of radius 14 m and height 3.5 m when the cost of its metal is Rs. 50 per cubic meter :
Q.9
The radii of the bases of two cylinders are in the ratio 3 : 4 and their height are in the ratio 4 : 3. The ratio of their volume is :
Q.10
If the height of a cylinder is increased by 15 percent and the radius of its base is decreased by 10 percent then by what percent will its curved surface area change ?
Q.11
A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire, is :
Q.12
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients ?
Q.13
The breadth of a room is twice its height and half its length. The volume of the room is 512 cu.m. The length of the room is :
Q.14
A rectangular water tank is 8 m high, 6 m long and 2.5 m wide. How many litres of water can it hold ?
Q.15
The radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 m2, what is the volume of the cylinder ?
Q.16
Some solid metallic right circular cones, each with radius of the base 3 cm and height 4 cm, are melted to form a solid sphere of radius 6 cm. The number of right circular cones is :
Q.17
Find the number of coins 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Q.18
For a sphere of radius 10 cm, What percent of the numerical value of its volume would be the numerical value of the surface area ?
Q.19
A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath. The height of the cone is :
Q.20
A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is :
Q.21
A closed box made of wood of uniform thickness has length, breadth and height 12 cm, 10 cm and 8 cm respectively. If the thickness of the wood is 1 cm, the inner surface area is :
Q.22
From a cube of side 8 m, a square hole of 3 m side is hollowed from end to end. What is the volume of the remaining solid ?
Q.23
The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rate of Rs. 8 and Rs. 9.50 per square metre is Rs. 1248. Find the dimensions of the box in metres.
Q.24
The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is :
Q.25
Total surface area of a cube whose side is 0.5 cm is :
Q.26
The dimensions of an open box are 52 cm × 40 cm × 29 cm. It thickness is 2 cm. If 1 cu.cm of metal used in the box weight 0.5 gm, then the weight of the box is :
Q.27
A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out ?
Q.28
If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one ?
Q.29
A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :
Q.30
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cylinder of base diameter 8 cm, then the height of the cylinder is :
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