CUBOID
Let length = l, breadth = b and height = h units. Then,
1. Volume = (l x b x h) cubic units.
2. Surface volume-and-surface-area = 2 (lb + bh + lh) sq. units.
3. Diagonal = √l2 X b2 X h2 units,
CUBE
Let each edge of a cube be of length a, Then,
1. Volume = a3 cubic units.
2. Surface volume-and-surface-area = 6a2 sq. units.
3. Diagonal = √3 a units,
CYLINDER
Let radius of base = r and Height (or length) = h. Then,
1. Volume = (πr2h) cubic units.
2. Curved surface volume-and-surface-area = = (2πrh) sq. units.
3. Total surface volume-and-surface-area = (2πrh + 2πr2) sq. units = 2πr (h + r) sq. units.
CONE
Let radius of base = r and Height = h. Then,
1. Slant height l = √h2 + r2 units,
2. Volume = (1/3 πr2h) cubic units.
3. Curved surface volume-and-surface-area = (πrl) sq. units.
4. Total surface volume-and-surface-area = (πrl + πr2) sq. units.
SPHERE
Let the radius of the sphere be r. Then,
1. Volume = (4/3 πr3h) cubic units.
2. Surface volume-and-surface-area = = (4πr2) sq. units.
HEMISPHERE
Let the radius of a hemisphere be r Then,
1. Volume = (2/3 πr3) cubic units.
2. Curved surface volume-and-surface-area = (2πr2) sq. units.
3. Total surface volume-and-surface-area = (3πr2) sq. units. Remember : 1 litre = 1000 cm3.