Mensuration (Part-6)

1. Two similar triangles have area 490 sq. cm. and 640 sq. cm. If the length of the one side of the first triangle is 21 cm, then what is the length of the corresponding side of the second triangle? [SSC CHSL 05/07/2024 (4th Shift)]

(a) 16 cm
(b) 14 cm
(c) 24 cm
(d) 21 cm

Correct Answer: (c) 24 cm

Solution:

2. The diameter of a roller is 35 cm and its length is 100 cm. It takes 200 complete revolutions to level a playground. Find the area of the playground in m² [SSC CHSL 05/07/2024 (4th Shift)]

(a) 220
(b) 2,20,00,000
(c) 1,10,000
(d) 110

Correct Answer: (a) 220

Solution:

3. The perimeter of a rectangle is 70 cm and its diagonal is 25 cm. The area of the rectangle is : [SSC CHSL 08/07/2024 (1st Shift)]

(a) 425 cm²
(b) 420 cm²
(c) 300 cm²
(d) 625 cm²

Correct Answer: (c) 300 cm²

Solution:

4. A solid sphere of radius 8 cm is melted and then recast into small spherical balls each of diameter 4 cm. Find the number of balls thus obtained (used π = 22/7) [SSC CHSL 08/07/2024 (1st Shift)]

(a) 64
(b) 48
(c) 32
(d) 24

Correct Answer: (a) 64

Solution:

5. If the radius of a sphere is increased by 3.5 cm, its surface area increases by 550 cm². What was the original radius of the sphere? (use π = 22/7) [SSC CHSL 08/07/2024 (2nd Shift)]

(a) 4 cm
(b) 4.5 cm
(c) 6 cm
(d) 3.5 cm

Correct Answer: (b) 4.5 cm

Solution:

6. The perimeter of a square whose area is the same as the area of a semi-circle of radius 2√2 cm is: [SSC CHSL 08/07/2024 (2nd Shift)]

(a) 8√π cm
(b) 8√2π cm
(c) 16√π cm
(d) 4√π cm

Correct Answer: (a) 8√π cm

Solution:

7. A metallic solid cuboid of dimensions 36cm × 22cm × 12cm is melted and recast in the form of cubes of side 6 cm. Find the number of the cubes so formed. [SSC CHSL 08/07/2024 (2nd Shift)]

(a) 45
(b) 46
(c) 43
(d) 44

Correct Answer: (d) 44

Solution:

8. The area of an isosceles right angled triangle is 16m². Its hypotenuse is_____ . [SSC CHSL 08/07/2024 (3rd Shift)]

(a) 0.8 m
(b) 8 m
(c) 4 m
(d) 8 cm

Correct Answer: (b) 8 m

Solution:

9. Find the cost of painting a ball that is in the shape of a sphere with a radius of 14 cm. The painting cost of the ball is ₹5 per square centimetre (take π = 22/7) [SSC CHSL 08/07/2024 (4th Shift)]

(a) ₹12,230
(b) ₹12,320
(c) ₹13,022
(d) ₹13,220

Correct Answer: (b) ₹12,320

Solution:

10. Two cubes, each of edge 5 cm, are joined face to face. Find the surface area of the cuboid thus formed. [SSC CHSL 08/07/2024 (4th Shift)]

(a) 250 cm²
(b) 300 cm²
(c) 125 cm²
(d) 200 cm²

Correct Answer: (a) 250 cm²

Solution:

Mensuration (Part-6)

1. Two similar triangles have area 490 sq. cm. and 640 sq. cm. If the length of the one side of the first triangle is 21 cm, then what is the length of the corresponding side of the second triangle? [SSC CHSL 05/07/2024 (4th Shift)]

2. The diameter of a roller is 35 cm and its length is 100 cm. It takes 200 complete revolutions to level a playground. Find the area of the playground in m² [SSC CHSL 05/07/2024 (4th Shift)]

3. The perimeter of a rectangle is 70 cm and its diagonal is 25 cm. The area of the rectangle is : [SSC CHSL 08/07/2024 (1st Shift)]

4. A solid sphere of radius 8 cm is melted and then recast into small spherical balls each of diameter 4 cm. Find the number of balls thus obtained (used π = 22/7) [SSC CHSL 08/07/2024 (1st Shift)]

5. If the radius of a sphere is increased by 3.5 cm, its surface area increases by 550 cm². What was the original radius of the sphere? (use π = 22/7) [SSC CHSL 08/07/2024 (2nd Shift)]

6. The perimeter of a square whose area is the same as the area of a semi-circle of radius 2√2 cm is: [SSC CHSL 08/07/2024 (2nd Shift)]

7. A metallic solid cuboid of dimensions 36cm × 22cm × 12cm is melted and recast in the form of cubes of side 6 cm. Find the number of the cubes so formed. [SSC CHSL 08/07/2024 (2nd Shift)]

8. The area of an isosceles right angled triangle is 16m². Its hypotenuse is_____ . [SSC CHSL 08/07/2024 (3rd Shift)]

9. Find the cost of painting a ball that is in the shape of a sphere with a radius of 14 cm. The painting cost of the ball is ₹5 per square centimetre (take π = 22/7) [SSC CHSL 08/07/2024 (4th Shift)]

10. Two cubes, each of edge 5 cm, are joined face to face. Find the surface area of the cuboid thus formed. [SSC CHSL 08/07/2024 (4th Shift)]

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