Surface Area and Volume of a Cube

Cube is a solid shape having 6 equal square faces.

Lateral surface area of a cube4l2
Total surface area of a cube6l2
The volume of a cubel3
Diagonal√3 l,  l = edge of the cube

Example

What is the capacity of a cubical vessel having each side of 7 cm?

Solution

Given side =  cm

So, Volume of the cubical vessel = l3

= (7)3 = 343 cm3.

Surface Area and volume of a Cuboid

Cuboid is a solid shape having 6 rectangular faces at a right angle.

Lateral surface area of a cuboid2h(l + b)
Total surface area of a cuboid2(lb + bh + lh)
Volume of a cuboidlbh
Diagonal\sqrt{\mathrm{l^2+b^2+h^2}}
l = length, b = breadth, h = height

Example

What is the surface area of a cereal box whose length, breadth and height is 20 cm, 8 cm and 30 cm respectively?

Solution

Given,

Length \text{= 20 cm}

Breadth \text{= 8 cm}

Height \text{= 30 cm}

Total surface area of the cereal box \text{= 2(lb + bh + lh)}

= 2(20 \times 8 + 8 \times 30 + 20 \times 30)

= 2(160 + 240 + 600)

= 2(1000) = 2000\ \text{cm}^2.

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