Mensuration (Part-9)

1. What is the volume of a cube if the perimeter of one face of the cube is 40 cm? [SSC CGL 17/07/2023 (3rd shift)]

(a) 1000 cm³
(b) 820 cm³
(c) 600 cm³
(d) 800 cm³

Correct Answer: (a) 1000 cm³

Solution:

2. A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are 3/2 cm and 2cm, respectively. Find the diameter of the third ball. [SSC CGL 17/07/2023 (4th shift)]

(a) 2.1 cm
(b) 3.3 cm
(c) 3 cm
(d) 2.5 cm

Correct Answer: (d) 2.5 cm

Solution:

3. The area of the sector of a circle of radius 12 cm is 32 π cm². Find the length of the corresponding arc of the sector. [SSC CGL 17/07/2023 (4th shift)]

Correct Answer: (a)

Solution:

4. The ratio of the length of each equal side and the third side of an isosceles triangle is 3:5. If the area of the triangle is 30√11 cm², then the length of the third side (in cm) is: [SSC CGL 18/07/2023 (2nd shift)]

(a) 10√6
(b) 5√6
(c) 13√6
(d) 11√6

Correct Answer: (a) 10√6

Solution:

5. A conical tent has a radius of 7 m and a vertical height of 24 m. How many full bags of rice can be emptied in it if the space occupied by the rice in each bag is 2 m³? [SSC CGL 19/07/2023 (1st shift)]

(a) 566
(b) 616
(c) 716
(d) 650

Correct Answer: (b) 616

Solution:

6. To have a surface area of 9π square units of a ball, what should be the diameter (in units) of the ball? [SSC CGL 19/07/2023 (3rd shift)]

(a) 2.5
(b) 2
(c) 1.5
(d) 3

Correct Answer: (d) 3

Solution:

7. A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is: [SSC CGL 20/07/2023 (2nd shift)]

(a) 6√2 cm
(b) 9 cm
(c) 6 cm
(d) 3√6 cm

Correct Answer: (b) 9 cm

Solution:

8. The width of a rectangle is 2 m less than its length. If the perimeter of the rectangle is 68 m, then what is the length (in metres) of the rectangle? [SSC CGL 20/07/2023 (4th shift)]

(a) 20
(b) 18
(c) 16
(d) 17

Correct Answer: (b) 18

Solution:

9. The length, breadth and height of a cuboid are in the ratio 1:2:3. The length, breadth and height of the cuboid are increased by 200%, 300% and 300%, respectively. Then compared to the original volume, the increase in the volume of the cuboid will be: [SSC CGL 20/07/2023 (4th shift)]

(a) 47 times
(b) 26 times
(c) 17 times
(d) 15 times

Correct Answer: (a) 47 times

Solution:

10. The volume of a cuboid is twice that of a cube. If the dimensions of the cuboid are (8m x 8m x 16m), the total surface area of the cube is: [SSC CGL 21/07/2023 (1st shift)]

(a) 316 m²
(b) 288 m²
(c) 324 m²
(d) 384 m²

Correct Answer: (d) 384 m²

Solution:

Mensuration (Part-9)

1. What is the volume of a cube if the perimeter of one face of the cube is 40 cm? [SSC CGL 17/07/2023 (3rd shift)]

2. A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are 3/2 cm and 2cm, respectively. Find the diameter of the third ball. [SSC CGL 17/07/2023 (4th shift)]

3. The area of the sector of a circle of radius 12 cm is 32 π cm². Find the length of the corresponding arc of the sector. [SSC CGL 17/07/2023 (4th shift)]

4. The ratio of the length of each equal side and the third side of an isosceles triangle is 3:5. If the area of the triangle is 30√11 cm², then the length of the third side (in cm) is: [SSC CGL 18/07/2023 (2nd shift)]

5. A conical tent has a radius of 7 m and a vertical height of 24 m. How many full bags of rice can be emptied in it if the space occupied by the rice in each bag is 2 m³? [SSC CGL 19/07/2023 (1st shift)]

6. To have a surface area of 9π square units of a ball, what should be the diameter (in units) of the ball? [SSC CGL 19/07/2023 (3rd shift)]

7. A solid cone with curved surface area twice its base area has slant height of 6√3 cm. Its height is: [SSC CGL 20/07/2023 (2nd shift)]

8. The width of a rectangle is 2 m less than its length. If the perimeter of the rectangle is 68 m, then what is the length (in metres) of the rectangle? [SSC CGL 20/07/2023 (4th shift)]

9. The length, breadth and height of a cuboid are in the ratio 1:2:3. The length, breadth and height of the cuboid are increased by 200%, 300% and 300%, respectively. Then compared to the original volume, the increase in the volume of the cuboid will be: [SSC CGL 20/07/2023 (4th shift)]

10. The volume of a cuboid is twice that of a cube. If the dimensions of the cuboid are (8m x 8m x 16m), the total surface area of the cube is: [SSC CGL 21/07/2023 (1st shift)]

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