a solid cylinder has total surface area 462sqcm. its curved surface area is one third of its total surface area. find the radius and height of the cylinder
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Radius 112
Height 234
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Answer:
TSA of cylinder=462
CSA of cylinder=1/3*462=154
CSA of cylinder=2πrh
2πrh=154
2*22/7*rh=154
rh=154*7/22*2
rh=49/2
r=49/2h
now put the value of 'r' in TSA of cylinder.
TSA of cylinder=2πr(r+h)
2πr(r+h)=462
2*22/7*49/2h(49/2h+h)=462
154/h(49+2h²/2h)=462
49+2h²/2h=462*h/154
49+2h²/2h=3h
49+2h²=6h²
49=4h²
h²=49/4
h=√49/4
h=7/2
We have found the value of 'h'.
so,r=49/2h
r=49/2*7/2
r=7
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