Question
Download Solution PDFIf the radius of the base of a right circular cylinder is decreased by 30% and its height is increased by 224%, then what is the percentage increase (closest integer) in its volume?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius decreased by 30% ⇒ New radius = 70% = 0.7r
Height increased by 224% ⇒ New height = 324% = 3.24h
Formula used:
Volume of cylinder = πr2h
% Increase = \(\left(\frac{\text{New Volume} - \text{Old Volume}}{\text{Old Volume}}\right) \times 100\)
Calculations:
New volume = π(0.7r)2 × 3.24h = πr2h × (0.49 × 3.24)
⇒ New Volume = πr2h × 1.5876
⇒ % Increase = (1.5876 - 1) × 100 = 58.76%
∴ Volume increases by approximately 59%
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