Volume and surface area

Cuboids:

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

1. Volume = (l × b × 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 = √3 a units.  

Cylinder:

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

1. Volume = (πr²h) cubic units.

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

3. Total surface area = (2πrh + 2πr²) sq. units.

                                        = 2πr(h + r) sq. units.

Cone:

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

1. Slant height, l = √(h² + r²) units.

2. Volume = (1 πr²h/3 cubic units.

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

4. Total surface area = (πrl + πr²) sq. units.

Sphere:

Let the radius of the sphere be r. Then

1. Volume = (4πr³/3) cubic units.

2. Surface area = (4πr²) sq. units.

Hemisphere:

Let the radius of a hemisphere be r. Then,

1. Volume = (2πr³/3) cubic units.

2. Curved surface area = (2πr²) sq. units.

3. Total surface area = (3πr²) sq. units. (curved surface + top circular surface)

Remember: 1 liter = 1000 cm³.