The ratio of curved surface area and total surafarcw area of circular cylinder is 1:2and total surface area is 616cm2 find bolume
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Sorry for the untidy work but I needed to speed up.. Hope this helps.
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Given :-
The ratio between the curved surface area and the total surface area of right circular cylinder is 1:2
To Find :-
Volume
Solution :-
We know that
CSA = 2πrh
TSA = 2πr(r + h)
CSA/TSA = 1/2
2πrh/2πr(r + h) = 1/2
h/r + h = 1/2
2(h) = r + h
2h = r + h
2h - h = r
h = r (1)
Now, ATQ
CSA = TSA/2
CSA = 616/2
CSA = 308 cm
CSA = 2πrh
- As r = h
CSA = 2πrr
CSA = 2πr²
308 = 2 × 22/7 × r²
308 = 44/7 × r²
308 × 7/44 = r²
49 = r²
√(49) = r
7 = r
As r = h
h = 7 cm
Now,
Volume of cylinder = πr²h
Volume = 22/7 × (7)² × 7
Volume = 22/7 × 49 × 7
Volume = 22 × 49
Volume = 1078 cm³
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