Aptitude - Volume and Surface Area

CUBOID

Let length = l, breadth = b and height = h units. Then

1. Volume = (l x b x h) cubic units.

2. Surface area = 2(lb + bh + lh) sq. units.

3. Diagonal = l² + b² + h² units.

CUBE

Let each edge of a cube be of length a. Then,

1. Volume = a³ cubic units.

2. Surface area = 6a² sq. units.

3. Diagonal = 3a units.

CYLINDER

Let radius of base = r and Height (or length) = h. Then,

1. Volume = (r²h) cubic units.

2. Curved surface area = (2rh) sq. units.

3. Total surface area = 2r(h + r) sq. units.

CONE

Let radius of base = r and Height = h. Then,

1. Slant height, l = h² + r² units.

2. Volume = r²h cubic units.

3. Curved surface area = (rl) sq. units.

4. Total surface area = (rl + r²) sq. units.

SPHERE

Let the radius of the sphere be r. Then,

1. Volume = r³ cubic units.

2. Surface area = (4r²) sq. units.

HEMISPHERE

Let the radius of a hemisphere be r. Then,

1. Volume = r³ cubic units.

2. Curved surface area = (2r²) sq. units.

3. Total surface area = (3r²) sq. units.

   Note: 1 litre = 1000 cm³.