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:

, Avg: 00:44 , 76%✓ 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?

, Avg: 00:33 , 50%✓ 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 )

, Avg: 00:59 , 69%✓ 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.

, Avg: 00:35 , 90%✓ 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?

, Avg: 01:46 , 90%✓ 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)?

, Avg: 01:10 , 57%✓ 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 \(\pi = \frac{22}{7}\) )

, Avg: 01:59 , 50%✓ 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?

, Avg: 00:49 , 100%✓ 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 )

, Avg: 02:19 , 66%✓ SSC CGL 2022

A)

1632.8

B)

1758.4

C)

1695.6

D)

1570.2