total surface area of cylinder is 462cm and its curved surface area is one third of total surface area find volume
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Answered by
3
TSA= 462 cm²
CSA= 1/3TSA
CSA= 1/3*462
CSA=154 cm²
2πrh=154
2×22/7×rh=154
44/7×rh=154
rh=7/44×154
rh=24.5
TSA=462 cm²
2πrh+2πr²=462 cm²
154+2πr²=462
2πr²=308
44/7×r²=308
r²=308×7/44
r²=49
r=7 cm
rh=24.5
h=24.5/r
h=24.5/7
h=3.5 cm
Volume=πr²h
Volume= 22/7×49×3.5
Volume=154×3.5
Volume= 539 cm³
Answered by
2
TSA=2πr(h+r)
462=2πr(h+r). (¡)
Now,CSA=2πrh
1/3×462=2πrh
154=2πrh. (¡¡)
Dividing equation (i) from (ii)
462/154=2πr(h+r)/2πrh
3=(h+r)/h
r=2h
Putting value of r in equation (i)
2×22/7×2h(h+2h)=462
h^2=462×7/22×2×6
h^2=12.25
h=3.5
Then,r=3.5×2=7
Volume = πr^2h
=22/7×7×7×3.5
=539cm^3
Hope it will help
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