Mensuration (Part-3)

1. A cylinder has a radius 8/π cm and its volume is 448cm³. What is the height of the cylinder (taken π = 22/7)? [SSC CHSL Tier II (18/11/2024)]

(a) 24 cm
(b) 21 cm
(c) 23 cm
(d) 22 cm

Correct Answer: (d) 22 cm

Solution:

2. The radii of the two spheres are in the ratio 4: 5. Their volume will be in the ratio: [SSC CHSL Tier II (18/11/2024)]

(a) 64: 125
(b) 125:64
(c) 16:25
(d) 4:5

Correct Answer: (a) 64: 125

Solution:

3. For making a toy, a hemisphere is attached at one end of a cylinder and a cone is attached at the other end of the cylinder. The cylinder, the cone and the hemisphere have a common radius of 4.2 cm. The height of the cylinder and that of the cone is 7 cm. Find the volume (in cm³) of the toy. (Use π = 1/22) [SSC CHSL Tier II (18/11/2024)]

(a) 358.8
(b) 762.255
(c) 672.672
(d) 863.25

Correct Answer: (c) 672.672

Solution:

4. The area of a regular hexagon is 2048√3 cm². What is the length (in cm) of each side of the hexagon ? [SSC MTS 30/09/2024 (Morning)]

Correct Answer: (b)

Solution:

5. A right circular cone of height h and radius R is cut by a plane parallel to the base at a distance h/4 from the base. The ratio of the curved surface areas of the resulting cone to the frustum is: [SSC MTS 30/09/2024 (Afternoon)]

(a) 7:16
(b) 16:9
(c) 16:7
(d) 9:7

Correct Answer: (d) 9:7

Solution:

6. What is the number of gold coins, each having a radius of 0.875 cm and a thickness of 2 mm, that need to be melted to create a cuboid with dimensions 5.5cm × 5cm × 3.5cm ? (Use π = 22/7) [SSC MTS 30/09/2024 (Evening)]

(a) 250
(b) 175
(c) 200
(d) 225

Correct Answer: (c) 200

Solution:

= 200

7. A cylindrical tank of height 10 m and radius 5 m has a small circular cut of 0.5 m radius on its top surface. What would be the total surface area of the tank ? [SSC MTS 01/10/2024 (Morning)]

(a) 599π/4 m²
(b) 156π m²
(c) 299π/2 m²
(d) 150π m²

Correct Answer: (a) 599π/4 m²

Solution:

8. A solid cylinder with a height of 8 units and a radius of 3.5 units is to be covered with a paper sheet. If the cost of the paper sheet is ₹40 per 5 square units, the cost (in) of covering the cylinder is _______ (Take π = 22/7) [SSC MTS 01/10/2024 (Afternoon)]

(a) 2268
(b) 1664
(c) 2024
(d) 1012

Solution:

9. A hemispherical bowl is 264 cm round at the brim. Suppose that the bowl is half-full of beverage. If the beverage is served in hemispherical glasses 6 cm in the diameter at the top, how many people would be served ? [SSC MTS 07/10/2024 (Morning)]

(a) 1170
(b) 1372
(c) 1270
(d) 1470

Correct Answer: (b) 1372

Solution:

10. What is the area of the remaining portion of a circle of radius 14 cm when a square with maximum possible area inscribed in it is removed from it? (Use π 22 = 22/7) [SSC MTS 07/10/2024 (Morning)]

(a) 518 cm²
(b) 520 cm²
(c) 224 cm²
(d) 616 cm²

Correct Answer: (c) 224 cm²

Solution:

Mensuration (Part-3)

1. A cylinder has a radius 8/π cm and its volume is 448cm³. What is the height of the cylinder (taken π = 22/7)? [SSC CHSL Tier II (18/11/2024)]

2. The radii of the two spheres are in the ratio 4: 5. Their volume will be in the ratio: [SSC CHSL Tier II (18/11/2024)]

4. The area of a regular hexagon is 2048√3 cm². What is the length (in cm) of each side of the hexagon ? [SSC MTS 30/09/2024 (Morning)]

5. A right circular cone of height h and radius R is cut by a plane parallel to the base at a distance h/4 from the base. The ratio of the curved surface areas of the resulting cone to the frustum is: [SSC MTS 30/09/2024 (Afternoon)]

6. What is the number of gold coins, each having a radius of 0.875 cm and a thickness of 2 mm, that need to be melted to create a cuboid with dimensions 5.5cm × 5cm × 3.5cm ? (Use π = 22/7) [SSC MTS 30/09/2024 (Evening)]

7. A cylindrical tank of height 10 m and radius 5 m has a small circular cut of 0.5 m radius on its top surface. What would be the total surface area of the tank ? [SSC MTS 01/10/2024 (Morning)]

8. A solid cylinder with a height of 8 units and a radius of 3.5 units is to be covered with a paper sheet. If the cost of the paper sheet is ₹40 per 5 square units, the cost (in) of covering the cylinder is _______ (Take π = 22/7) [SSC MTS 01/10/2024 (Afternoon)]

9. A hemispherical bowl is 264 cm round at the brim. Suppose that the bowl is half-full of beverage. If the beverage is served in hemispherical glasses 6 cm in the diameter at the top, how many people would be served ? [SSC MTS 07/10/2024 (Morning)]

10. What is the area of the remaining portion of a circle of radius 14 cm when a square with maximum possible area inscribed in it is removed from it? (Use π 22 = 22/7) [SSC MTS 07/10/2024 (Morning)]

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