A cylinder is such that the sum of its height and circumference of its base is 10m. Find the greatest volume of the cylinder
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Answer:
28/27π m³ = 0.33 m³
Step-by-step explanation:
A cylinder is such that the sum of its height and circumference of its base is 10m. Find the greatest volume of the cylinder
circumference of base = 2πR
Height = H
H + 2πR = 10
=> H = 10 - 2πR
Volume of Cylinder = πR²H
= πR² (10 - 2πR)
= 10πR² - 20π²R³
dV/dR = 20πR - 60π²R²
dV/dR = 0
=> 20πR - 60π²R² = 0
=> 60π²R² = 20πR
=> R = 1/3π
d²V/dR² = 20π - 120π²R
putting R = 1/3π
= 20π - 40π
= - 20π
=> R = 1/3π will give miaximum Volume
Volume = πR² (10 - 2πR) = (π/9π²)(10 - 2π/3π)
= (1/9π)( 10 - 2/3)
= (1/9π)( 28/3)
= 28/27π m³
= 0.33 m³
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