three metal cubes whose edge measures 3cm ,4cm and 5cm are melted tk form a single cube. Find the edge of the new cube
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Your Question :
Three cubes of metal each of edges 3cm, 4cm and 5cm are melted and made into a single cube. Find the length of an edge of the new cube.
Given Information :
- Edges of three cubes of metal are 3cm, 4cm and 5cm respectively.
- Three cubes are melted and made into a single cube.
To Find :
- the volume of the new cube.
- the length of an edge of the new cube.
Solution :
The volume of the first cube is V¹ = (3 cm)³ = 27 cm³.
The volume of the second cube is V² = (4 cm)³ = 64 cm³.
The volume of the third cube is V³ = (5 cm)³ = 125cm³.
∴ The volume of the new cube →
: ⟼ V = V¹ + V² + V³
ㅤㅤ ⟼ 27 cm³ + 64 cm³ + 124 cm³
ㅤㅤ ⟼ 216 cm³.
∴ The length of an edge of the new cube →
³√V = ³√216 cm³ = ³√6 × 6 × 6 cm = 6cm
Therefore :
∴ The length of an edge of the new cube is 6 cm.
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