Question

Three metal cubes whose edge measure 3cm 4cm and 5cm respectively are melted to form a single cube

Answer 1

vol.of 1st cube =3×3×3
=============27cm³

vol. of 2nd cube=4×4×4
===============64cm³

vol. of 3rd cube =5×5×5
===============125cm³

vol. of the new cube=vol.1+vol.2+vol.3
======27+64+125
======216cm³
answer - the volume of new cube is 216cm³

Answer 2

Correct Question:

Three metal cubes whose edges measure 3cm, 4cm and 5 cm respectively are melted to form a single cube. Find its edge. Also, find the surface area of the new cube.

AnswEr:

Let x cm be the edge of the new cube. Then,

• Volume of the new cube = Sum of the volumes of three cubes

$\implies \tt {x}^{3} = {3}^{3} + {4}^{3} + {5}^{3} \\ \\ \tt = 27 + 64 + 125 \\ \\ \implies \tt {x}^{3} = 216 \\ \\ \implies \tt {x}^{ 3} = {6}^{3} \\ \\ \implies \tt \: x = 6cm$

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• $\mathfrak\orange{Surface\:area\:the\:new\:cube-}$

$\tt = 6 {x}^{2} = 6 \times {(6)}^{2} \: {cm}^{2} = 216 \: {cm}^{2}$

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