Question

total surface area of cylinder is 462cm and its curved surface area is one third of total surface area find volume

Answer 1

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

Answer 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