The sum of the altitude and the base radius of a cylinder is #63 cm#. The radius is #4/5# as long as the altitude. Calculate the surface area volume of the cylinder?

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Answer 1 · 2016-05-28T01:52:09

Let y be the altitude, and x be the radius.

#x + y = 63#

#4/5y = x#

#4/5y + y = 63#

#(9y)/5 = 63#

#9y = 63 xx 5#

#9y = 315#

#y = 35#

#x + 35 = 63#

#x = 63 - 35#

#x = 28#

The surface area of a cylinder is given by #S.A = 2r^2pi + 2rhπ#

The radius, r, measures 28 cm.

Therefore, #S.A = 2(28)^2pi + 2(28)(35)π#

#S.A = 1568pi + 1960pi#

#S.A = 3528pi# c#m^2#

As for the volume, the volume of a cylinder is given by #V = r^2π xx h#

#V = 28^2pi xx 35#

#V = 27440pi# c#m^3#

Hopefully this helps!