Volume and Surface Area Test 1
The perimeter of one face of a cube is 20 cm. Its volume must be
  • 105 cm3
  • 125 cm3
  • 200 cm3
  • 400 cm3
Explanation: Perimeter of one face of the cube = 20 cm o A cube has square faces, so the perimeter of one face is 4 × side. o Let the side length be s. o 4s = 20 o s = 5 cm Volume of the cube = s³ o 5³ = 125 cm³ Ans: (B) 125 cm³.
The dimensions of a room are 15 m, 10 m and 8 m. The volume of a bag is 2.25 m3. The maximum number of bags that can be accommodated in the room is
  • 531
  • 532
  • 533
  • 550
Explanation: • Volume of the room = Length × Breadth × Height = 15 × 10 × 8 = 1200 m³ • Volume of one bag = 2.25 m³ • Maximum number of bags = Total volume / Volume of one bag = 1200 / 2.25 = 533.33 Since the number of bags must be a whole number, the maximum possible is 533. Ans: (C) 533.
The radius of the base and height of a cone are 3 cm and 5 cm respectively whereas the radius of the base and height of a cylinder are 2 cm and 4 cm respectively. The ratio of the volume of cone to that of the cylinder is
  • 1 : 3
  • 15 : 8
  • 15 : 10
  • 15 : 16
    • Explanation: Volume of a Cone The volume of a cone is given by: V = 1/3πr2h For the given cone: • Radius (r) = 3 cm • Height (h) = 5 cm Vcone = 1/3π(3)2(5) = 1/3π x 9 x 5 = 45/3π = 15π Volume of a Cylinder The volume of a cylinder is given by: V = πr2h For the given cylinder: • Radius (r) = 2 cm • Height (h) = 4 cm Vcylinder = π(2)2(4) = π×4×4 = 16π Ratio of Volume of Cone to Cylinder Vcone / Vcylinder = 15π/16π = 15/16 Ans: 15 : 16