Mensuration (Part-6)

21. The ratio of the outer and the inner circumference of a circular path is 7:6. If the path is 45 m wide, then what is the radius (in m) of the inner circle? [SSC CHSL 10/07/2024 (2nd Shift)]

(a) 240
(b) 270
(c) 150
(d) 120

Correct Answer: (b) 270

Solution:

Let the radius of outer circle
be R and inner circle be r.
2πR : 2πr = 7 : 6 ⇒ R : r = 7 : 6
Diffrence (7 - 6) = 1 unit
1 unit = 45m
Hence, radius of inner circle (6 unit)
= 45 × 6 = 270 m

22. A solid metallic cube having surface area of 54 cm² is melted to form smaller cubes of surface area 8/12 cm² each. Find the number of smaller cubes. [SSC CHSL 10/07/2024 (4th Shift)]

(a) 512
(b) 343
(c) 216
(d) 729

Correct Answer: (d) 729

Solution:

23. Find the surface area (in cm²) of a cardboard box in the shape of a cuboid whose length is 60 cm, breadth is half its length and height is one-third of its breadth. [SSC CHSL 11/07/2024 (1st Shift)]

(a) 2700
(b) 10800
(c) 8100
(d) 5400

Correct Answer: (d) 5400

Solution:

24. From a circle of radius r units, the largest equilateral triangle is cut out. What is the length (in units) of the side of the triangle? [SSC CHSL 11/07/2024 (1st Shift)]

(a) r/√2
(b) √2r
(c) √3r
(d) r/√3

Correct Answer: (c) √3r

Solution:

25. If the area of a rhombus is 70 m² and its height is 5 m, its perimeter is______ . [SSC CHSL 11/07/2024 (2nd Shift)]

(a) 64 m
(b) 35 m
(c) 56 m
(d) 25 m

Correct Answer: (c) 56 m

Solution:

26. The measure of each side of an equilateral triangle is 16 cm. What is the ratio of its perimeter to the sum of its medians? [SSC CHSL 11/07/2024 (2nd Shift)]

(a) √3 : 2
(b) 2√3 : 1
(c) 2 : √3
(d) 1 : 2√3

Correct Answer: (c) 2 : √3

Solution:

27. A hemispherical bowl is made of silver and has an inner diameter of 4 cm if the thickness of silver is 0.5 cm. Find the volume of silver used in making the bowl correct to two places of decimals (use π = 3.14) [SSC CHSL 11/07/2024 (2nd Shift)]

(a) 15.69 cm³
(b) 51.96 cm³
(c) 15.96 cm³
(d) 51.69 cm³

Correct Answer: (c) 15.96 cm³

Solution:

28. The volume of the rectangular block is 12288 m³. Its dimensions are in the ratio of 4:3:2. If the entire surface is polished at the rate 2 paise per m²,then find the total cost of polishing : [SSC CHSL 11/07/2024 (4th Shift)]

(a) ₹44.42
(b) ₹11.14
(c) ₹66.56
(d) ₹33.28

Correct Answer: (c) ₹66.56

Solution:

29. A hemispherical bowl is 88 cm round the brim. Assuming it to be full, how many persons may be served from it in hemispherical glasses, 7 cm in diameter at the top ? (Where π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

(a) 74
(b) 68
(c) 64
(d) 70

Correct Answer: (c) 64

Solution:

30. The chord length of a chord made on an arc of a circle is equal to the radius of the circle. The length of the arc is______(in units), if the radius of the circle is 21 units. (Take π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

(a) 20
(b) 22
(c) 24
(d) 21

Correct Answer: (b) 22

Solution:

Mensuration (Part-6)

21. The ratio of the outer and the inner circumference of a circular path is 7:6. If the path is 45 m wide, then what is the radius (in m) of the inner circle? [SSC CHSL 10/07/2024 (2nd Shift)]

22. A solid metallic cube having surface area of 54 cm² is melted to form smaller cubes of surface area 8/12 cm² each. Find the number of smaller cubes. [SSC CHSL 10/07/2024 (4th Shift)]

23. Find the surface area (in cm²) of a cardboard box in the shape of a cuboid whose length is 60 cm, breadth is half its length and height is one-third of its breadth. [SSC CHSL 11/07/2024 (1st Shift)]

24. From a circle of radius r units, the largest equilateral triangle is cut out. What is the length (in units) of the side of the triangle? [SSC CHSL 11/07/2024 (1st Shift)]

25. If the area of a rhombus is 70 m² and its height is 5 m, its perimeter is______ . [SSC CHSL 11/07/2024 (2nd Shift)]

26. The measure of each side of an equilateral triangle is 16 cm. What is the ratio of its perimeter to the sum of its medians? [SSC CHSL 11/07/2024 (2nd Shift)]

27. A hemispherical bowl is made of silver and has an inner diameter of 4 cm if the thickness of silver is 0.5 cm. Find the volume of silver used in making the bowl correct to two places of decimals (use π = 3.14) [SSC CHSL 11/07/2024 (2nd Shift)]

28. The volume of the rectangular block is 12288 m³. Its dimensions are in the ratio of 4:3:2. If the entire surface is polished at the rate 2 paise per m²,then find the total cost of polishing : [SSC CHSL 11/07/2024 (4th Shift)]

29. A hemispherical bowl is 88 cm round the brim. Assuming it to be full, how many persons may be served from it in hemispherical glasses, 7 cm in diameter at the top ? (Where π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

30. The chord length of a chord made on an arc of a circle is equal to the radius of the circle. The length of the arc is______(in units), if the radius of the circle is 21 units. (Take π = 22/7) [SSC CPO 27/06/2024 (1st Shift)]

Related Posts