Question

The total surface area of a cube is 1350 m². Find its volume in litres.​

Answer 1

Given :-

Total surface area of a cube = 1350m²

To find :-

Volume in litres.

TOTAL SURFACE AREA = 6a²

Where 'a' denotes the edge.

Substituting the values,

1350m² = 6 × a²

By transposing 6 to the LHS (Left Hand Side)

$\dfrac{1350}{6} = {a}^{2}$

$225 = {a}^{2}$

By transposing the power,

$\sqrt{225} = a$

$15m = a$

Now that we know the edge, we have to find the volume.

VOLUME = a³

Where 'a' denotes edge.

Volume = 15m³

Volume = 3,375m³

1 m³ = 1000l

Therefore,

3375m³ = 3375 × 1000l

Volume in litres = 3375000 litres.

Some more formulas :-

Lateral surface area of a cube = 4a²

Total surface area of a cuboid = 2(lb + bh + hl)

Lateral surface area of a cuboid = 2h(l+b)

Volume of a cuboid = length × breadth × height

Total surface area of a cylinder = 2πrh + 2πr² =≥ 2πr(h+r)

Lateral surface area of a cylinder = 2πrh

Volume of a cylinder = πr²h