VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

1. A hollow right circular cylindrical vessel of volume V whose diameter is equal to its height, is completely filled with water. A heavy sphere of maximum possible volume is then completely immersed in the vessel. What volume of water remains in the vessel? [2019 (II) Evening Shift]

Correct Answer: (b) V/3
Solution:Let the radius of cylinder = r

2. The areas of three adjacent faces of a cuboid are x y , and z. If V is the volume of the cuboid, then which one of the following is correct? [2019 (II) Evening Shift]

Correct Answer: (b) V² = xyz
Solution:

3. Two cylinders of equal volume have their heights in the ratio 2 : 3. What is the ratio of their radii? [2019 (II) Evening Shift]

Correct Answer: (b) √3 : √2
Solution:

4. A right circular cylinder has a diameter of 20 cm and its curved surface area is 1000 cm² . What is the volume of the cylinder? [2019 (II) Evening Shift]

Correct Answer: (a) 4000 cm³
Solution:


5. A hollow sphere of external and internal diameters 6 cm and 4 cm, respectively is melted into a cone of base diameter 8 cm. What is the height of the cone? [2019 (II) Evening Shift]

Correct Answer: (a) 4.75 cm
Solution:The external radius of hollow sphere

6. A solid metallic cylinder of height 10 cm and radius 6 cm is melted to make two cones in the ratio of volume 1 : 2 and of same height as 10 cm. What is the percentage increase in the flat surface area? [2019 (II) Evening Shift]

Correct Answer: (b) 50%
Solution:Radius of cylinder(r) = 6 cm, Height of cylinder (h) = 10 cm



7. A thin rod of length 24 feet is cut into rods of equal size and joined, so as to form a skeleton cube. What is the area of one of the faces of the largest cube thus constructed? [2019 (II) Evening Shift]

Correct Answer: (d) 4 square feet
Solution:


8. Three copper spheres of radii 3 cm, 4 cm and 5 cm are melted to form a large sphere. What is its radius? [2019 (II) Evening Shift]

Correct Answer: (d) 6 cm
Solution:Sphere of radii 3 cm, 4 cm and 5 cm are melted to form a large sphere of
radius r.

9. The volume of a hemisphere is 155232 cm³ . What is the radius of the hemisphere? [2019 (II) Evening Shift]

Correct Answer: (b) 42 cm
Solution:Let the radius of hemisphere be ‘r’ cm.

10. A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are 6 cm and 12 cm, respectively. If the height of the bucket is 7 cm, what is the capacity of the bucket? [2019 (II) Evening Shift]

Correct Answer: (b) 462 cm³
Solution:Given,