21)

A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into n toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:

SSC CGL 2019

A)

27

B)

64

C)

48

D)

54

22)

The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick, What is the total surface area (in \(cm^2\)) of the vessel?

SSC CGL 2019

A)

\(612.75\pi\)

B)

\(468.75\pi\)

C)

\(600.2\pi\)

D)

\(600.5\pi\)

23)

A sector of radius 10.5 cm with the central angle \(120^0\) is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in \(cm^3\)) of the cone so formed?

SSC CGL 2019

A)

\({343\sqrt2\over6}\pi\)

B)

\({343\sqrt3\over6}\pi\)

C)

\({343\sqrt3\over12}\pi\)

D)

\({343\sqrt2\over12}\pi\)

24)

The area of the base of a right circular cone is \(400\pi\) and its height is 15 cm. The curved surface area of the cone (in \(cm^2\)) is:

SSC CGL 2019

A)

\(480\pi\)

B)

\(500\pi\)

C)

\(450\pi\)

D)

\(560\pi\)

25)

The base of a right prism is a triangle with sides 20 cm, 21 cm and 29 cm. If its volume is 7560 \(cm^3\), then its lateral surface area (in \(cm^2\)) is:

SSC CGL 2019

A)

2484

B)

2556

C)

2520

D)

2448

26)

A cylindrical vessel of radius 3.5 m is full of water. If 15400 litres of water is taken out from it, then the drop in the water level in the vessel will be:

SSC CGL 2019

A)

72 cm

B)

40 cm

C)

35 cm

D)

60 cm

27)

A solid metallic sphere of radius 8 cm is melted and drawn into a wire of uniform cross-section. If the length of the wire is 24 m, then its radius (in mm) is:

SSC CGL 2019

A)

6

B)

5

C)

\(5\frac{1}{3}\)

D)

\(6\frac{2}{3}\)

28)

The base of a right pyramid is an equilateral triangle with side 8 cm, and the height of the pyramid is \(24\sqrt3\) cm. The volume (in \(cm^3\)) of the pyramid is:

SSC CGL 2019

A)

1152

B)

480

C)

576

D)

384

29)

If the diameter of the base of a right circular cylinder is reduced by \(33\frac{1}{3}\)% and its height is doubled, then the volume of the cylinder will :

SSC CGL 2019

A)

increase by \(1\frac{1}{9}\)%

B)

remain unchanged

C)

increase by \(11\frac{1}{9}\)%

D)

decrease by \(11\frac{1}{9}\)%

30)

A right circular solid cone of radius 3.2 cm and height 7.2 cm is melted and recast into a right circular cylinder of height 9.6 cm. What is the diameter of the base of the cylinder?

SSC CGL 2019

A)

4.2 cm.

B)

4.5 cm.

C)

3.5 cm.

D)

3.2 cm.