Question
Download Solution PDFMelting a metal ball of radius 3 units, 26 identical dice and a ball of radius 1 units are made. What is the side of the dice?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Melting a metal ball of radius 3 units, 26 identical dice and a ball of radius 1 unit are made.
Formula used:
Volume of sphere = (4/3)πr3
Volume of cube = a3
Calculation:
Volume of original ball = Volume of 1ball + volume of 26 cube
⇒ (4/3) π (3)3 = (4/3) π (1)3 + 26 × a3
⇒ (4/3) π (3)3 - (4/3) π (1)3 = 26 × a3
⇒ (4/3) π × 27 - (4/3) π × 1 = 26 × a3
⇒ (4/3) π (27 - 1) = 26 × a3
⇒ (4/3) π × 26 = 26 × a3
⇒ (4/3) π = a3
⇒ a3 = 4/3 × 22/7 = 88/21 = 4.19
⇒ a = 3√ 4.19 ≈ 1.6 units
∴ The correct answer is option (4).
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