Mensuration (Part-8)

1. Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long. [SSC CPO 03/10/2023 (3rd Shift)]

(a) 164 cm²
(b) 144 cm²
(c) 160 cm²
(d) 120 cm²

Correct Answer: (d) 120 cm²

Solution:

2. The total surface area of a square-based right pyramid is 1536 m², of which 37.5% is the area of the base of the pyramid. What is the volume (in m³) of this pyramid ? [SSC CPO 04/10/2023 (1st Shift)]

(a) 3108
(b) 3048
(c) 3072
(d) 3144

Correct Answer: (c) 3072

Solution:

3. If the diameter of a sphere is reduced to its half, then the volume would be: [SSC CPO 04/10/2023 (2nd Shift)]

(a) reduced by 1/8 of the former volume
(b) increased by 1/4 of the former volume
(c) reduced by 1/4 of the former volume
(d) increased by 1/8 of the former volume

Correct Answer: (a) reduced by 1/8 of the former volume

Solution:

4. The heights of two cones are in the ratio 7:5 and their diameters are in the ratio 10:21. What is the ratio of their volumes ? (Where π 22/7) [SSC CPO 04/10/2023 (2nd Shift)]

(a) 17:21
(b) 14:19
(c) 20: 63
(d) 26:47

Correct Answer: (c) 20: 63

Solution:

5. The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere. [SSC CPO 04/10/2023 (3rd Shift)]

(a) 25π
(b) 50π/4
(c) 25π/4
(d) 75π/4

Correct Answer: (d) 75π/4

Solution:

6. The height and the radius of the base of a right circular cone are in the ratio of 12:5. If its volume is 314 cm³, then what is the slant height of the cone ? [SSC CPO 05/10/2023 (1st Shift)]

(a) 11 cm
(b) 14 cm
(c) 12 cm
(d) 13 cm

Correct Answer: (d) 13 cm

Solution:

7. A right square pyramid having lateral surface area is 624 cm². If the length of the diagonal of the square is 24√2, then the volume of the pyramid is: [SSC CPO 05/10/2023 (1st Shift)]

(a) 780 cm³
(b) 1150 cm³
(c) 1083 cm³
(d) 960 cm³

Correct Answer: (d) 960 cm³

Solution:

8. A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm. [SSC CPO 05/10/2023 (1st Shift)]

(a) 1.6 cm
(b) 8.75 cm
(c) 8 cm
(d) 6.75 cm

Correct Answer: (d) 6.75 cm

Solution:

9. What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively? [SSC CPO 05/10/2023 (2nd Shift)]

(a) 250 m²
(b) 400 m²
(c) 200 m²
(d) 300 m²

Correct Answer: (d) 300 m²

Solution:

10. Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q What is the ratio between the volumes of P and Q? [SSC CPO 05/10/2023 (2nd Shift)]

(a) 8:1
(b) 16:1
(c) 64:1
(d) 32:1

Correct Answer: (c) 64:1

Solution:

Mensuration (Part-8)

1. Find the area of a rhombus if the perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm long. [SSC CPO 03/10/2023 (3rd Shift)]

2. The total surface area of a square-based right pyramid is 1536 m², of which 37.5% is the area of the base of the pyramid. What is the volume (in m³) of this pyramid ? [SSC CPO 04/10/2023 (1st Shift)]

3. If the diameter of a sphere is reduced to its half, then the volume would be: [SSC CPO 04/10/2023 (2nd Shift)]

4. The heights of two cones are in the ratio 7:5 and their diameters are in the ratio 10:21. What is the ratio of their volumes ? (Where π 22/7) [SSC CPO 04/10/2023 (2nd Shift)]

5. The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere. [SSC CPO 04/10/2023 (3rd Shift)]

6. The height and the radius of the base of a right circular cone are in the ratio of 12:5. If its volume is 314 cm³, then what is the slant height of the cone ? [SSC CPO 05/10/2023 (1st Shift)]

7. A right square pyramid having lateral surface area is 624 cm². If the length of the diagonal of the square is 24√2, then the volume of the pyramid is: [SSC CPO 05/10/2023 (1st Shift)]

8. A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm. [SSC CPO 05/10/2023 (1st Shift)]

9. What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively? [SSC CPO 05/10/2023 (2nd Shift)]

10. Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q What is the ratio between the volumes of P and Q? [SSC CPO 05/10/2023 (2nd Shift)]

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