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Mensuration (Part-3)
📆 August 8, 2025
Total Questions: 50
21.
A hemispherical container of total surface area 7392 cm² is filled with oil. However, 1/4 of the container is empty. This oil is to be transferred in small hemispherical bottles having radius of 6.3 cm. How many bottles will be required (rounded off to the nearest whole number)? (Take π = 22/7)
[SSC MTS 14/10/2024 (Evening)]
(a) 351
(b) 66
(c) 75
(d) 156
Correct Answer:
(b) 66
Solution:
22.
A cone of radius 16 cm and height 12 cm is cut, parallel to the base, at some height closer to the top. If the ratio of the heights of the solids is 1: 3, then the ratio of the total surface areas of the two solids formed is approximately given by:
[SSC MTS 17/10/2024 (Morning)]
(a) 9:143
(b) 1:8
(c) 2:15
(d) 7:180
Correct Answer:
(a) 9:143
Solution:
23.
A conical cavity is drilled in a solid circular cylinder of 7 cm height and 48 cm base diameter. The height and base diameter of the cone are the same as those of the cylinder. What is the total surface area of the remaining solid ?
[SSC MTS 17/10/2024 (Afternoon)]
(a) 1512π cm²
(b) 1076π cm²
(c) 1420π cm²
(d) 1654π cm²
Correct Answer:
(a) 1512π cm²
Solution:
24.
The side of a square exceeds the side of another square by 3 cm and the sum of the areas of the two squares is 225 cm². Find the sum of the perimeter (in cm) of both squares.
[SSC MTS 17/10/2024 (Evening)]
(a) 84
(b) 74
(c) 64
(d) 94
Correct Answer:
(a) 84
Solution:
25.
The external curved surface area of a metallic hemispherical bowl is 308 cm². If the density of metal is 8.7 gm per cm³, then the mass of the bowl is equal to: (Take π = 22/7)
[SSC MTS 18/10/2024 (Morning)]
(a) 6254.2 gm
(b) 6252.4 gm
(c) 5262.4 gm
(d) 5264.2 gm
Correct Answer:
(b) 6252.4 gm
Solution:
26.
From a square with area a² another square made on mid points of the sides of the square is removed. What is the area left in the squaге?
[SSC MTS 18/10/2024 (Morning)]
(a)
(b)
(c)
(d)
Correct Answer:
(a)
Solution:
27.
In a lead pipe 4.2 m long, the external diameter is 5.4 cm and the thickness of the pipe is 3 mm. Find the weight of the pipe, if 1 cm³ of lead mass is 25 grams. (Use π = 22/7)
[SSC MTS 18/10/2024 (Afternoon)]
(a) 54.90 kg
(b) 45.09 kg
(c) 59.40 kg
(d) 50.49 kg
Correct Answer:
(d) 50.49 kg
Solution:
28.
A solid sphere of iron having radius 15 cm is to be melted and recast in the shape of a cylindrical pipe having internal and external radii 4 cm and 6 cm, respectively. Find the length (in m) of the pipe thus formed.
[SSC MTS 18/10/2024 (Evening)]
(a) 2.15
(b) 2.25
(c) 2.45
(d) 2.35
Correct Answer:
(b) 2.25
Solution:
29.
The sum of the radius and slant height of a cone is square of the height of the cone, while the difference between the radius and slant height is 1 cm only. What is the total surface area (in cm²) of the cone having height of 9 cm? (Take π = 22/7) (Rounded off to 2 decimal places)
[SSC MTS 21/10/2024 (Morning)]
(a) 10,437.43
(b) 11,282.85
(c) 10,182.86
(d) 10,128.85
Correct Answer:
(a) 10,437.43
Solution:
30.
A cylinder of radius 10 cm and height 30 cm is cut, parallel to the base, into two pieces of different sizes. The total surface area of the larger piece formed is 70% of that of the given cylinder. The smaller piece is melted and made into a sphere. The radius (in cm) of the sphere is:
[SSC MTS 21/10/2024 (Morning)]
(a)
(b)
(c)
(d)
Correct Answer:
(b)
Solution:
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