The ratio of diameter and height of a right circular cylinder is 4 : 3. If diameter of the cylinder get reduced by 25% then its total surface area reduced to 318.5 square meter. What is the circumference of the base of the cylinder. (a) 28 pi m (b) 14 pi m (c) 35 pi m (d) 7 pi m (e) none of these
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Let the diameter be 4y and height be 3y
Since the diameter = 4y
=> Radius = 4y/2 = 2y
So the total surface area = 2πr(h + r)
=> Total surface area = 2π2y(3y + 2y)
=> Total surface area = 4yπ(5y)
=> Total surface area = 20y²π
Now the diameter is decreased by 25%
=> New diameter = 4y - 25% of 4y
=>
New diameter = 3y
=> Radius = 3y/2
=> Total surface area =
=>
Given that new total surface area is 318.5 less than the old surface area
=>
Now radius = 2y
=> Radius =
Now circumference = 2πr
=>
Answer is 28 √π
Option a
There should be 28 root pi though
Since the diameter = 4y
=> Radius = 4y/2 = 2y
So the total surface area = 2πr(h + r)
=> Total surface area = 2π2y(3y + 2y)
=> Total surface area = 4yπ(5y)
=> Total surface area = 20y²π
Now the diameter is decreased by 25%
=> New diameter = 4y - 25% of 4y
=>
New diameter = 3y
=> Radius = 3y/2
=> Total surface area =
=>
Given that new total surface area is 318.5 less than the old surface area
=>
Now radius = 2y
=> Radius =
Now circumference = 2πr
=>
Answer is 28 √π
Option a
There should be 28 root pi though
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