1. The perimeter of one face of a cube is 20 cm. Its volume must be
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.
2. 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
• 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.
3. 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
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