Solid Geometry

Q.

A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

1. 72

2. 96

3. 48

4. 24

5. none

Q.

The largest four-digit number which is a perfect cube is :

1. 8000

2. 9261

3. 9999

4. 8999

5. 9761

Q.

The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is:

1. 60π cm²

2. 68π cm³

3. 120π cm²

4. 136π cm²

5. 146π cm²

Q.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

1. 2:1

2. 3:2

3. 25:18

4. 27:20

Q. How a aeroplane fly in the sky and it is turning out

Q.

A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

1. 49 m²

2. 25 m²

3. 55 m²

4. 56 m²

Q.

The number of bricks, each measuring 25 cm $\times$ 12.5 cm $\times$ 7.5 cm, required to construct a wall 6 m long, 5 m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is:

1. 6080

2. 8120

3. 3040

4. 5740

Q. If a cube of maximum possible volume is cut off from a solid sphere of diameter d, then the volume of the remaining (waste) material of the sphere would be equal to:

1. None of these
2. $\frac{d^3}{3}(\pi -\frac{d}{2})$
   
3. $\frac{d^3}{3}(\frac{\pi }{2}-\frac{1}{\sqrt{3}})$
   
4. $\frac{d^2}{4}(\sqrt{2}-\pi )$

Q.

Three cubes with sides in the ratio 3:4:5 are melted to form a single cube whose diagonal is $12\sqrt{3}$cm, the sides of the cubes are:

1. 3 cm, 4 cm, 5 cm

2. 6 cm, 8 cm, 10 cm

3. 9 cm, 12 cm, 15 cm

4. 12 cm, 16 cm, 20 cm

5. None of these

Q.

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?

1. 32 m³

2. 40 m³

3. 36 m³

4. 44 m³

5. 66 m³

Q.

If the height of a cone is doubled and radius of the base remains the same, then the ratio of the volume of the given cone to that of the second cone will be:

1. 1:8

2. 1:2

3. 2:1

4. 8:1

5. 1:3

Q. Two spheres of radii 6 cm and 1 cm are inscribed inside a right circular cone. The bigger sphere touches the smaller sphere and also the base of the cone. What is the height of the cone?

1. 14 cm
2. 12 cm
3. 85/6 cm
4. 72/5 cm

Q.

The length of a rectangle is 5 cm more than its width and the area is 50cm${}^2$. Find the length.

1. 10 cm

2. 5 cm

3. 7 cm

4. 25 cm

Q.

If the both the radius and height of a right circular cone are increased by 20%, its volume will be increased by:

1. 60%

2. 72.8%

3. 80%

4. 40%

Q.

If the height of a cylinder becomes $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ of the original height and the radius is doubled, then which of the following will be true?

1. Volume of the cylinder will be doubled.

2. Volume of the cylinder will remain unchanged.

3. Volume of the cylinder will be halved.

4. The volume of the cylinder will be$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ the original volume.

Q.

If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone is:

1. Increases by 25%

2. Increases by 50%

3. Decreased by 45%

4. Remain unaltered

5. Decreases by 25%

Q. A cone is made of a sector with a radius of 14 cm and and angle of ${60}^{\circ }$. What is total suface area of the cone?

1. None of these
2. $191.87c{m}^2$
3. $119.78c{m}^2$
4. $196.5c{m}^2$

Q. The edge of a cube is increased by 100%, the surface area of the cube is increased by:

1. 100%
2. 200%
3. 300%
4. 400%

Q.

The slant height of a conical mountain is 2.5 km and the area of its base is $1.54k{m}^2$. The height of the mountain is:

1. 4.2 km

2. 2.2 km

3. 2.4 km

4. 3.1 km

Q.

The surface area of a square pyramid is 85 square meters. The side length of the base is 5 meters. What is the slant height?

Q. A rectangular water reservoir is 15 m by 12 m at the base. Water flows into it through a pipe whose cross-section is 5 cm by 3 cm at the rate of 16 m per second. Find the height to which the water will rise in the reservoir in 25 minutes:

1. 0.2 m
2. 2 cm
3. 0.5 m
4. None of these

Q.

A 3x3x3 cube has three square holes, each with a 1 by 1 cross-section running from the centre of each face to the centre of the opposite face. The total surface area (in square units) of the resulting solid is:

1. 48

2. 72

3. 78

4. 24

Q.

A rectangular water tank is 80 m $\times$ 40 m. Water flows into it through a pipe 40 sq.cm at the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half an hour?

1. 5 cm

2. 1/2 cm

3. 4/9 cm

4. 5/8 cm

5. 1 cm

Q. Five spheres are kept in a cone in such a way that each sphere touch each other and also touch the lateral surface of the cone, this is due to increasing radius of the spheres starting from the vertex of the cone. The radius of the smallest sphere is 16 cm.

If the radius of the fifth (i.e., largest) sphere be 81 cm, then find the radius of the third (i.e., middlemost) sphere.

1. 36 cm
2. Data insufficient
3. $25\sqrt{3}cm$
4. 25 cm

Q. A solid wooden toy in the shape of a right circular cone is mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

1. $266c{m}^3$
2. $104c{m}^3$
3. $162c{m}^3$
4. $427c{m}^3$

Q. What is the total surface area of a triangular prism whose height is 30 m and the sides of whose base are 21 m, 20 m and 13 m, respectively?

1. 1652 sq. m
2. 1542 sq. m
3. 1872 sq. m
4. 1725 sq. m

Q.

The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to:

1. Twice the volume of the box

2. The volume of the box

3. The square of the volume of the box

4. The cube root of the volume of the box

5. None of these

Q.

The volume of a cylinder is $48.125c{m}^3$, which is formed by rolling a rectangular paper sheet along the length of the paper. If a cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting out the square of side 0.5 cm from each of the four corners of the paper sheet, then what is the volume of this box?

1. None of these

2. $20c{m}^3$

3. $38c{m}^3$

4. $19c{m}^3$

Q.

A big cube of side 8 cm is formed by rearranging together 64 small but identical cubes each of side 2 cm. Further, if the corner cubes in the topmost layer of the big cube are removed, what is the change in total surface area of the big cube?

1. Remains the same as previously

2. $32c{m}^2$, decreases

3. $16c{m}^2$, decreases

4. $48c{m}^2$, decreases

Q. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of cone, as well as cylinder is 21 cm. The cylindrical part is 80 cm high and conical part is 16 cm high.
Find the weight of the pillar, if 1 cm3 of iron weighs 8.45 g :

1. 999.39 kg
2. 111 kg
3. 1001 kg
4. 989 kg