Question

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 a uniform thickness of  1 cm?​

Answer 1

Given :- 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 a uniform thickness of 1 cm ?

Solution :-

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.)

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Answer 2

Given : 160 L of molten metal is cast into 20 identical cubes,

To Find : how many litres of paint will be required to paint all the cubes completely with a uniform thickness of 1 cm

Solution:

160 L of molten metal for 20 cubes

Hence 8L  for 1 cube

=> 8000 cm³  for  1 cube

=> Side of cube = ∛8000 = 20 cm  

Total Surface area of cube = 6 * 20²  = 2400 cm²

Thickness at each surface  = 1 cm

Hence Volume of Paint Required in one cube =  2400 * 1 = 2400 cm³

= 2.4 L

Volume of Paint Required in  20 cubes = 20 * 2.4 = 48 Litre

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