A large cube is formed from the material obtained by melting three sma

1.	A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cms side. What is of the ratio the total surface areas of the smaller cubes and the large cube?1). 2 ∶ 12). 3 ∶ 23). 25 ∶ 184). 27 ∶ 20
Answer» We know that, volume of a cube = a³ Volume of cubes of 3 cm, 4 cm and 5 cm sides = 3³+ 4³+ 5³ cm³ = 27 + 64 + 125 = 216 cm³ Surface area of the smaller cubes = 6(9 + 16 + 25) = 6 × 50 = 300 cm² Since the large cube is obtained by melting the three smaller cubes, THUS, volume of larger cube = sum of VOLUMES of three smaller cubes = 216 cm³ Side of larger cube $(a)$ = ?216 cm = 6 cm Surface area of larger cube = 6 × a² cm², where a = length of each side of a cube = 6 × 6² = 216 cm² $(\therefore \frac{{surface\;area\;of\;smaller\;cubes}}{{surface\;area\;of\;larger\;cube\;}}\; = \;\frac{{300}}{{216}} = \;\frac{{25}}{{18}})$

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cms side. What is of the ratio the total surface areas of the smaller cubes and the large cube?1). 2 ∶ 12). 3 ∶ 23). 25 ∶ 184). 27 ∶ 20

Answer»

We know that, volume of a cube = a³

Volume of cubes of 3 cm, 4 cm and 5 cm sides = 3³+ 4³+ 5³ cm³

= 27 + 64 + 125 = 216 cm³

Surface area of the smaller cubes = 6(9 + 16 + 25) = 6 × 50 = 300 cm²

Since the large cube is obtained by melting the three smaller cubes,

THUS, volume of larger cube = sum of VOLUMES of three smaller cubes = 216 cm³

Side of larger cube $(a)$ = ?216 cm = 6 cm

Surface area of larger cube = 6 × a² cm², where a = length of each side of a cube

= 6 × 6² = 216 cm²

$(\therefore \frac{{surface\;area\;of\;smaller\;cubes}}{{surface\;area\;of\;larger\;cube\;}}\; = \;\frac{{300}}{{216}} = \;\frac{{25}}{{18}})$

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