Mensuration

Three cubes of 4 cm each is kept beside each other to form a cuboid. The breadth of the resulting cuboid is:
1. 12 cm
2. 8 cm
3. 4 cm
4. None of these
During conversion of a solid from one shape to another, the volume of the new shape will:
1. Increase
2. Remain unaltered
3. Decrease
4. Double up
A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
1. 2r cm
2. r cm
3. h cm
4. 2h cm
The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is:
1. $\sqrt{26} c m$
2. 5 cm
3. $\sqrt{65} c m$
4. 25 cm
The total surface area of a hemispherical solid having radius 7 cm is:
1. 462 $c m^{2}$
2. 294 $c m^{2}$
3. 588 $c m^{2}$
4. 154 $c m^{2}$
A solid formed on revolving a right angled triangle about its height is:
1. Cylinder
2. Sphere
3. Two cones
4. Right circular cone
The surface area of a sphere is 616 $c m^{2}$ . Its radius is:
1. 7 cm
2. 14 cm
3. 21 cm
4. 28 cm
A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is:
1. 2 : 1
2. 3 : 1
3. 2 : 3
4. 3 : 2
The volume of a sphere is 4851 cm $c m^{3}$ . Its diameter is:
1. 3.5 cm
2. 7 cm
3. 14 cm
4. 21 cm
A piece of paper is in the shape of a semi-circular region of radius 10 cm. It is rolled to form a right circular cone. The slant height is:
1. 5 cm
2. 10 cm
3. 15 cm
4. 20 cm
The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are:
1. 9 : 25
2. 5 : 3
3. 9 : 5
4. 3 : 25
The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is:
1. 55 $c m^{2}$
2. 110 $c m^{2}$
3. 220 $c m^{2}$
4. 440 $c m^{2}$
If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is:
1. $4 π r^{2}$
2. $3 π r^{2}$
3. $5 π r^{2}$
4. $6 π r^{2}$
A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that $\frac{1}{8} t h$ space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is:
1. 142244
2. 142396
3. 142496
4. 142596
A solid piece of iron in the form of cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is:
1. 21 cm
2. 23 cm
3. 25 cm
4. 19 cm
A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas?
1. 90.72 $c m^{2}$
2. 256.72 $c m^{2}$
3. 330.30 $c m^{2}$
4. 514.28 $c m^{2}$
The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is:
1. 4.2
2. 2.1
3. 8.1
4. 1.05
In a swimming pool measuring 90 m × 40 m, 150 men take a dip. If the average displacement of water by a man is 8 $m^{3}$ , then rise in water level is:
1. 27.33 cm
2. 30 cm
3. 31.33 cm
4. 33.33 cm
Given that 1 $c m^{3}$ of marble weighs 25 g, the weight of a marble block of 28 cm in width and 5 cm thick, is 112 kg. The length of the block is:
1. 36 cm
2. 37.5 cm
3. 32 cm
4. 26.5 cm
A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is:
1. $\sqrt{π} : \sqrt{6}$
2. $\sqrt{6} : \sqrt{π}$
3. $\sqrt{π} : \sqrt{3}$
4. $\sqrt{3} : \sqrt{π}$
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm):
1. 3
2. 4
3. 5
4. 6
The shape of a gilli, in the gilli-danda game, is a combination of:
1. Two cylinders
2. A cone and a cylinder
3. Two cones and a cylinder
4. Two cylinders and a cone
A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be:
1. 6
2. 11
3. 33
4. 40
A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute is:
1. 31500 $m^{3}$
2. 3150 $m^{3}$
3. 3150000 $m^{3}$
4. 6300 $m^{3}$
A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is:
1. 0.36 $c m^{3}$
2. 0.35 $c m^{3}$
3. 0.34 $c m^{3}$
4. 0.33 $c m^{3}$
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is:
1. 4 cm
2. 3 cm
3. 2 cm
4. 6 cm
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is:
1. 32.7 litres
2. 33.7 litres
3. 34.7 litres
4. 31.7 litres
Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is:
1. 3 : 4
2. 4 : 3
3. 9 : 16
4. 16 : 9
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 is:
1. 350
2. 400
3. 450
4. 500
The shape of a glass (tumbler) is usually in the form of:
1. A cone
2. Frustum of a cone
3. A cylinder
4. A sphere
A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is:
1. 1 : 2
2. 2 : 1
3. 1 : 4
4. 4 : 1
Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is:
1. 350 $c m^{2}$
2. 340 $c m^{2}$
3. 400 $c m^{2}$
4. 360 $c m^{2}$
The ratio of the volume of a cube to that of a sphere which will fit inside the cube is:
1. $36 : π$
2. $6 : π$
3. $\sqrt{6} : π$
4. $\sqrt{36} : π$
Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is:
1. 1 : 9
2. 1 : 3
3. 1 : 27
4. None of these
A joker’s cap is in the form of a right circular cone of base radius 7 cm and the slant height is 25 cm. The area of the cap is:
1. 570 $c m^{2}$
2. 560 $c m^{2}$
3. 550 $c m^{2}$
4. 540 $c m^{2}$

Mensuration

Quiz