Question
Download Solution PDFIf the edge of a cube is increased by 4 cm, the volume will increases by 988 cm3. Then the original length of each edge of the cube is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAs we know,
Volume of cube = a3 (a = edge length of the cube)
New side of the cube = (a + 4)
⇒ New volume of cube = (a + 4)3
According to the question
(a + 4)3 – a3 = 988
⇒ a3 + 64 + 3 × a × 4 (a + 4) – a3 = 988
⇒ 3 × 4 × a × (a + 4) = 988 – 64
⇒ a (a + 4) = 924/12
⇒ a2 + 4a – 77 = 0
⇒ a2 + 11a – 7a – 77 = 0
⇒ (a + 11)(a – 7) = 0
⇒ a = 7 (∵ Value of length cannot be negative)
∴ Side of the cube is 7 cm
Other Method:
Let side of the cube be 7 (from the option), then
⇒ Volume of cube = 73 = 343 cm3
New side of the cube = (7 + 4) = 11 cm
⇒ New volume of cube = 113 = 1331 cm3
∴ Volume decreased by = 1331 – 343 = 988 cm3 (satisfied)Last updated on Jun 2, 2025
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