Question

Question No:1
If 160 L of molten
metal is cast into 20
identical cubes, how
many litres of paint
will be required to
paint all the cubes
completely with
uniform thickness of
1 cm?
a​

Answer 1

given that, 160 litre of molten metal is melted and cast into 20 identical cubes.

So, we can say that,

→ volume of 20 identical cubes = 160 litre .

we know that, 1 litre = 1000 cm³.

→ volume of 20 identical cubes = 1000 * 160 = 160000 cm³.

Therefore,

→ volume of one cube = (160000)/20 = 8000cm³.

Now, we know that,

volume of cube = (side)³

So,

→ (side)³ = 8000

→ (side)³ = (20)³

cube root both sides ,

→ side = 20cm.

we conclude that , each side of all 20 identical cube is 20 cm.

Now, we know that,

Total surface area of cube = 6 * (side)² .

So,

→ TSA of one cube = 6 * (20)² = 6 * 400 = 2400 cm².

Now, we have given that, thickness at each surface = 1 cm.

Therefore,

→ volume of paint required for one cube = (TSA) * Thickness at each surface = 2400 * 1 = 2400cm³.

Hence,

→ volume of paint required for 20 cubes = 2400 * 20 = 48000cm³.

Again,

→ 1000 cm³ = 1 litre

→ 1 cm³ = (1/1000) litre

→ 48000cm³ = (48000/1000) = 48 Litre (Ans.)