Question

If 640 L of molten metal is cast into 10 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

Answer:

➠GIVEN :640 L of molten metal is cast into 10 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:

640 L of molten metal for10 cubes

Hence 64L for 1 cube

=> 64000 cm³ for 1 cube

=> Side of cube = ∛64000 = 40 cm

Total Surface area of cube = 6 × 40² = 9600 cm²

Thickness at each surface = 1 cm

Hence Volume of Paint Required in one cube = 9600 × 1 = 9600 cm³

=9.6 L

Volume of Paint Required in 10 cubes = 10 × 9.6 = 96 Litre

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Answer 2

Volume of paint required to paint all the 10 cubes completely is 96 L.

Given :

Total volume of molten metal = 640 L

No.of identical cubes = 10

Thickness of paint = 1cm

To find :

Volume of paint required to paint all the cubes completely with a uniform thickness of 1 cm

Solution :

640 L = 640000 cm^3

Volume of molten metal in 1 cube = 640000/10

= 64000 cm^3

Length of side of the cube = √64000

= 40 cm

Total surface area of a cube = 6a^2 where a is the side of the cube

Total surface area = 6 × 40^2

= 6 × 1600

= 9600 cm^2

Thickness of 1 side to paint = 1cm

Hence , volume of paint required to paint 1 cube = 9600 × 1

= 9600 cm^3 = 9.6L

Volume of paint required to paint 10 cubes = 9.6 × 10 L

= 96 L

Hence, Volume of paint required to paint all the 10 cubes completely is 96 L.

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