Question
Download Solution PDFThe radius of the base of a cylinder is increased from 4 cm to 16 cm, but its curved surface area remains unchanged. If the initial height of the cylinder was 4 cm, what will be its new height?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Initial radius (r) = 4 cm
New radius (R) = 16 cm
Initial height (h) = 4 cm
New height = H cm
Both curved surface area of the cylinder remains unchanged.
Formula Used:
Curved Surface Area of cylinder = 2πrh
Where, r = Radius of cylinder
h = Height of cylinder
Calculation:
Initial curved surface area = 2 × π × 4 × 4
= 32π cm2
New curved surface area = 2 × π × 16 × H
= 32πH cm2
As, Initial curved surface area = New curved surface area
⇒ 32π = 32πH
⇒ H = 1 cm
Hence, the new height of the cylinder is 1 cm.
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