the total surface area of a solid cylinder is 231 cm2 and its curved surface area is 2/3 of the total surface area. find the volume of the cylinder.
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Given that total surface area of a solid cylinder = 231cm^2.
Given that curved surface area = 2/3 * Total surface area.
2pirh = 2/3 * 231
2pirh = 154 --------------- (1)
pirh = 154/2
pirh = 77
h = 77/pi -------------- (2).
We know that Total surface area of a solid cylinder = 2pir^2 + 2pirh
231 = 2pir^2 + 154
2pir^2 = 77
2 * 22/7 * r^2 = 77
r^2 = 539/44
r^2 = 49/4
r = 7/2 ------------------- (3)
We know that volume of the cylinder = pir^2h
= pir^2 * 77/pir
= 77 * r
= 77 * 7/2
= 539/2
= 269.5cm^3.
Therefore the volume of the cylinder = 269.5cm^3.
Hope this helps!
Given that curved surface area = 2/3 * Total surface area.
2pirh = 2/3 * 231
2pirh = 154 --------------- (1)
pirh = 154/2
pirh = 77
h = 77/pi -------------- (2).
We know that Total surface area of a solid cylinder = 2pir^2 + 2pirh
231 = 2pir^2 + 154
2pir^2 = 77
2 * 22/7 * r^2 = 77
r^2 = 539/44
r^2 = 49/4
r = 7/2 ------------------- (3)
We know that volume of the cylinder = pir^2h
= pir^2 * 77/pir
= 77 * r
= 77 * 7/2
= 539/2
= 269.5cm^3.
Therefore the volume of the cylinder = 269.5cm^3.
Hope this helps!
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