Mensuration (Part-4)

1. What is the perimeter (in cm, rounded off to one decimal place) of the sector of a circle with a radius of 10 cm and of angle 30°? (Use π = 3.14) [SSC CGL 09/09/2024 (3rd Shift)]

(a) 20.4
(b) 35.7
(c) 82.8
(d) 25.2

Correct Answer: (d) 25.2

Solution:

2. If a right circular cone of height 24 cm has a volume of 1232cm³, then the total surface area of the cone is: (Use π = 22/7): [SSC CGL 10/09/2024 (1st Shift)]

(a) 806cm²
(b) 704cm²
(c) 904cm²
(d) 608cm²

Correct Answer: (b) 704cm²

Solution:

3. A rectangular piece of paper is 50 cm long and 22 cm wide. If a cylinder is formed by rolling the paper along its breadth, then the volume of the cylinder is: [SSC CGL 11/09/2025 (3rd Shift)]

(a) 2,125cm³
(b) 1,925cm³
(c) 2,025cm³
(d) 1,825cm³

Correct Answer: (b) 1,925cm³

Solution:

4. A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with the square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard. [SSC CGL 11/09/2024 (1st Shift)]

(a) 877
(b) 944
(c) 388
(d) 407

Correct Answer: (d) 407

Solution:

5. The inner and outer radii of a circular track are 28 m and 25 m, respectively. The cost (in ₹) of levelling the track at ₹28 per m² is: (Use π = 22/7) [SSC CGL 11/09/2024 (1st Shift)]

(a) 15,421
(b) 13,992
(c) 11,229
(d) 17,355

Correct Answer: (b) 13,992

Solution:

6. If the perimeter of an equilateral triangle is 36 units, then its area is (in square units): [SSC CGL 11/09/2024 (1st Shift)]

(a) 144√2
(b) 36√2
(c) 144√3
(d) 36√3

Correct Answer: (d) 36√3

Solution:

7. If the ratio of the areas of two similar triangles is 25:144, the ratio of their corresponding sides is: [SSC CGL 11/09/2024 (2nd Shift)]

(a) 5:12
(b) 5:144
(c) 25:12
(d) 12:5

Correct Answer: (a) 5:12

Solution:

8. A cuboid of dimensions 50 cm, 150 cm, 175 cm can be divided into how many identical largest cubes? [SSC CGL 11/09/2024 (3rd Shift)]

(a) 75
(b) 84
(c) 85
(d) 90

Correct Answer: (b) 84

Solution:

9. The height of a cylinder is 20 cm. The lateral surface area is 1760 cm². Its volume is: [SSC CGL 12/09/2024 (1st Shift)]

(a) 12032 cm³
(b) 12302 cm³
(c) 12203 cm³
(d) 12320 cm³

Correct Answer: (d) 12320 cm³

Solution:

10. Two cylinders have the radii of their bases in the ratio 4:5 and their heights are in the ratio 5:7. Find the ratio of their curved surface areas. [SSC CGL 12/09/2024 (2nd Shift)]

(a) 5:4
(b) 4:7
(c) 1:2
(d) 4:5

Correct Answer: (b) 4:7

Solution:

Mensuration (Part-4)

1. What is the perimeter (in cm, rounded off to one decimal place) of the sector of a circle with a radius of 10 cm and of angle 30°? (Use π = 3.14) [SSC CGL 09/09/2024 (3rd Shift)]

2. If a right circular cone of height 24 cm has a volume of 1232cm³, then the total surface area of the cone is: (Use π = 22/7): [SSC CGL 10/09/2024 (1st Shift)]

3. A rectangular piece of paper is 50 cm long and 22 cm wide. If a cylinder is formed by rolling the paper along its breadth, then the volume of the cylinder is: [SSC CGL 11/09/2025 (3rd Shift)]

4. A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with the square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard. [SSC CGL 11/09/2024 (1st Shift)]

5. The inner and outer radii of a circular track are 28 m and 25 m, respectively. The cost (in ₹) of levelling the track at ₹28 per m² is: (Use π = 22/7) [SSC CGL 11/09/2024 (1st Shift)]

6. If the perimeter of an equilateral triangle is 36 units, then its area is (in square units): [SSC CGL 11/09/2024 (1st Shift)]

7. If the ratio of the areas of two similar triangles is 25:144, the ratio of their corresponding sides is: [SSC CGL 11/09/2024 (2nd Shift)]

8. A cuboid of dimensions 50 cm, 150 cm, 175 cm can be divided into how many identical largest cubes? [SSC CGL 11/09/2024 (3rd Shift)]

9. The height of a cylinder is 20 cm. The lateral surface area is 1760 cm². Its volume is: [SSC CGL 12/09/2024 (1st Shift)]

10. Two cylinders have the radii of their bases in the ratio 4:5 and their heights are in the ratio 5:7. Find the ratio of their curved surface areas. [SSC CGL 12/09/2024 (2nd Shift)]

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