Question
Download Solution PDFA cube is having surface area of 5400 square units. Its volume would increase approximately ______ if the side is increased by 5 units.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Surface area of the cube = 5400 square units.
Side increment = 5 units.
Formula Used:
Surface area of a cube = 6a2
Volume of a cube = a3
Calculation:
Let the side of the cube be a units.
Surface area = 6a2
⇒ 6a2 = 5400
⇒ a2 = 5400 / 6
⇒ a2 = 900
⇒ a = 30 units
New side of the cube = a + 5 = 30 + 5 = 35 units
Original volume = a3 = 303
⇒ 303 = 27000 cubic units
New volume = (a + 5)3 = 353
⇒ 353 = 42875 cubic units
Increase in volume = New volume - Original volume
⇒ Increase in volume = 42875 - 27000
⇒ Increase in volume = 15875 cubic units
Approximate increase in volume = 0.59 × 27000
⇒ 15870 cubic units
The volume would increase approximately 59% .
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