Two metal cubes each of side 5 cm and 9 cm are melted and recast into a single cuboid of length 61 cm and breadth 7 cm. What is the height of the newly formed cuboid?
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Answer:
45 + 427
= 472 is the correct answer
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Understanding
Given,
Upon melting and recasting, 2 Cubes of side 5cm and 9cm, a Cuboid of length 61cm and breadth 7cm. We can find that,
V of Cube 1 + V of Cube 2 = V of Cuboid 1
(V - Volume)
Volume of Cube
Volume of Cube = S × S × S
S = 5 cm
Volume of Cube 1 = 5 cm × 5 cm × 5 cm
= 125 cm³
Volume of Cube 2 = 9 cm × 9 cm × 9 cm
= 729 cm³
Addition of Volumes
125 cm³ + 729 cm³
= 854 cm³
Volume of Cuboid
Volume of Cuboid = L × B × H
L = 61 cm
B = 7 cm
H = ?
(LET ' H ' be Height of Cuboid)
Volume of Cuboid 1 = 61 cm × 7 cm × H cm
It was given that V of Cuboid 1 = V of Cube 1 + V of Cube 2
= (427 × H) cm³ = 854 cm³
(Transversing of 427 to RHS)
= H cm = 854cm³ / 427 cm
= H = 2 cm
So, the Height (H) of the Cuboid is 2 cm
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