Mensuration

1. At what angle is the arc length half the perimeter of the circle? [SSC CGL 17/09/2024 (1st Shift)]

(a) 120°
(b) 180°
(c) 90°
(d) 270°

Correct Answer: (b) 180°

Solution:

2. What is the central angle of a sector of a circle whose area and perimeter are, respectively, equal to 209 cm² and 63 cm if it is given that its radius is a non-negative integer (roundup to one decimal place)? [SSC CGL 10/09/2024 (3rd Shift)]

(a) 55.5°
(b) 53.5°
(c) 49.5°
(d) 51.5°

Correct Answer: (c) 49.5°

Solution:

3. The area of a square is 16x² + 40x + 25 square units. Find the perimeter of the square. [SSC CGL 10/09/2024 (3rd Shift)]

(a) 3(10x + 8)
(b) 3(8x + 10)
(c) 2(10x + 8)
(d) 2(8x + 10)

Correct Answer: (d) 2(8x + 10)

Solution:

4. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the sides of 3 cm to form a cone. The volume of the cone so formed is: [SSC CGL 10/09/2024 (2nd Shift)]

(a) 20π cm³
(b) 16π cm³
(c) 25π cm³
(d) 28π cm³

Correct Answer: (b) 16π cm³

Solution:

5. Find the area (in cm²) of the sector whose perimeter is 64/3 cm and central angle is 60º. (Use π = 22/7) [SSC CGL 09/09/2024 (3rd Shift)]

(a) 47/3
(b) 77/3
(c) 68/3
(d) 85/3

Correct Answer: (b) 77/3

Solution:

6. A cuboid with dimensions 20cm, 12cm, and 10 cm is cut into 8 identical pieces by 3 cuts. What will be the total surface area of all the pieces? [SSC CHSL 10/07/2024 (3rd Shift)]

(a) 2440cm²
(b) 1220cm²
(c) 3360cm²
(d) 1680cm²

Correct Answer: (a) 2440cm²

Solution:

7. A rectangle with the largest area is cut out of a circle with radius 5 units. What is the area of the remaining portion? [SSC CHSL 10/07/2024 (1st Shift)]

(a) 25(2π-3)
(b) 25(2π-5)
(c) 25(π-3)
(d) 25(π-2)

Correct Answer: (d) 25(π-2)

Solution:

8. A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder. If their radii are in the ratio 3: 1, then the volume of the smaller cylinder is approximately______ % of the larger cylinder (the smaller cylinder % has its radius and height smaller when compared to the larger). [SSC CHSL 09/07/2024 (1st Shift)]

(a) 10.16
(b) 8.86
(c) 7.28
(d) 9.52

Correct Answer: (d) 9.52

Solution:

9. The inner and outer radii of a hemispherical wooden bowl are 6 cm and 8 cm, respectively. Its entire surface has to be polished and the cost of polishing π cm² is Rs.50. How much will it cost to polish the bowl? [SSC CHSL 08/07/2024 (4th Shift)]

(a) Rs.11,600
(b) Rs.11,400
(c) Rs.10,000
(d) Rs.12,000

Correct Answer: (b) Rs.11,400

Solution:

10. Which of the following statements is INCORRECT about the circle? [SSC CHSL 08/07/2024 (4th Shift)]

Correct Answer: (c)

Solution:

Mensuration

1. At what angle is the arc length half the perimeter of the circle? [SSC CGL 17/09/2024 (1st Shift)]

2. What is the central angle of a sector of a circle whose area and perimeter are, respectively, equal to 209 cm² and 63 cm if it is given that its radius is a non-negative integer (roundup to one decimal place)? [SSC CGL 10/09/2024 (3rd Shift)]

3. The area of a square is 16x² + 40x + 25 square units. Find the perimeter of the square. [SSC CGL 10/09/2024 (3rd Shift)]

4. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the sides of 3 cm to form a cone. The volume of the cone so formed is: [SSC CGL 10/09/2024 (2nd Shift)]

5. Find the area (in cm²) of the sector whose perimeter is 64/3 cm and central angle is 60º. (Use π = 22/7) [SSC CGL 09/09/2024 (3rd Shift)]

6. A cuboid with dimensions 20cm, 12cm, and 10 cm is cut into 8 identical pieces by 3 cuts. What will be the total surface area of all the pieces? [SSC CHSL 10/07/2024 (3rd Shift)]

7. A rectangle with the largest area is cut out of a circle with radius 5 units. What is the area of the remaining portion? [SSC CHSL 10/07/2024 (1st Shift)]

9. The inner and outer radii of a hemispherical wooden bowl are 6 cm and 8 cm, respectively. Its entire surface has to be polished and the cost of polishing π cm² is Rs.50. How much will it cost to polish the bowl? [SSC CHSL 08/07/2024 (4th Shift)]

10. Which of the following statements is INCORRECT about the circle? [SSC CHSL 08/07/2024 (4th Shift)]

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