1)

A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

SSC CGL 2022

A)

6

B)

4

C)

2

D)

5

2)

A 35 cm high bucket in the form of a frustum is full of water. Radii of its lower and upper ends are 12 cm and 18 cm, respectively. If water from this bucket is poured in a cylindrical drum, whose base radius is 20 cm, then what will be the height of water (in cm) in the drum?

SSC CGL 2022

A)

20.50

B)

19.95

C)

18.25

D)

16.25

3)

What is the difference in the volume (in cm³) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm? (Use π = 22/7 )

SSC CGL 2022

A)

1078

B)

704

C)

205

D)

924

4)

If the volume of a sphere is equal to that of a cylinder having the same radius, then find the ratio of the radius to the height of the cylinder.

SSC CGL 2022

A)

3 ∶ 4

B)

2 ∶ 3

C)

1 ∶ 2

D)

3 ∶ 5

5)

How many small solid spheres each of 5 mm radius can be made out of a metallic solid cone whose base has radius 21 cm and height 30 cm?

SSC CGL 2022

A)

25000

B)

26460

C)

32000

D)

18260

6)

A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic sphere of radius 12 cm is dropped into it. What will be the increase in the level of water in the vessel (in cm)?

SSC CGL 2022

A)

72

B)

9

C)

2.25

D)

27

7)

The curved surface area of a right circular cylinder is 616 cm² and the area of its base is 38.5 cm². What is the volume (in cm³) of the cylinder? (Take \(\pi = \frac{22}{7}\) )

SSC CGL 2022

A)

1078

B)

1408

C)

1243

D)

1155

8)

Let x cm² be the surface area and y cm³ be the volume of a sphere such that y = 14x. What is the radius (in cm) of the sphere?

SSC CGL 2022

A)

51

B)

42

C)

68

D)

102

9)

A hemispherical depression of diameter 4 cm is cut out from each face of a cubical block of sides 10 cm. Find the surface area of the remaining solid (in cm²). (Use \(\pi = \frac{22}{7} \))

SSC CGL 2022

A)

112\(\frac{4}{7}\)

B)

675\(\frac{3}{7}\)

C)

900\(\frac{4}{7}\)

D)

713\(\frac{1}{7}\)

10)

The circumference of the base of a right circular cylinder is 62.8 cm and its volume is 8792 cm² . What is the curved surface ( in cm² ) of the cylinder? (Take π = 3.14 )

SSC CGL 2022

A)

1632.8

B)

1758.4

C)

1695.6

D)

1570.2