Question
Download Solution PDFA cube of side 15 cm is cut into 27 small cubes. Then find the ratio of the lateral surface area of the large cube to the total surface area of one of the small cubes.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side of cube = 15 cm
Formula:
Volume of cube = a3
Calculation:
Volume of cube = 15 × 15 × 15
Volume of small cube = (15 × 15 × 15)/27 = 125 cm3
Side of small cube = ∛125
⇒ ∛(5 × 5 × 5)
⇒ 5 cm
Total surface area of small cube = 6 × 52
⇒ 6 × 25
⇒ 150 cm2
Lateral surface area of large cube = 4 × 152
⇒ 4 × 225
⇒ 900 cm2
∴ Required ratio = 900 : 150 = 6 : 1
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