The height of a right circular cylinder is twice its radius. If the height would be 6 times its radius, then the volume of the cylinder would be greater by 539 cubic dm. Calculate the height of the cylinder.
WBBSE
Class X
Mathematics
Right Circular Cylinder
4
2022
Given: height = 2r; if height = 6r, volume increases by 539 dm³.
Initial volume = πr²h = πr²(2r) = 2πr³
New volume = πr²h = πr²(6r) = 6πr³
Increase in volume = 6πr³ – 2πr³ = 4πr³
ATP: Increase in volume = 539
⇒ 4πr³ = 539
⇒ r³ = 539 × {7\over 22 × 4}
⇒ r³ = {343\over 8}
⇒ r = 3.5 dm
Height (actual) = 2r = 7 dm
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