A solid cylinder has TSA of 462 sq. cm if CSA is one third. Find the volume of the cylinder.
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As in ques CSA = 1/3 TSA
CSA = 1/3 × 462
CSA = 154 cm²
Then TSA of Cylinder = 2πr(r+h)
462 = 2πr(h+r) ......(1)
Also CSA of Cylinder = 2πrh
154 = 2πrh ......(2)
Dividing (1) and (2)
462/154 = 2πr(h+r)/2πrh
3 = (h+r)/h
3h = h+r
r = 2h ......(3)
Substituting (3) in (2)
154 = 2πrh
154 = 2 × 22/7 × 2h × h
2h² = 154 × 7/22 × 1/2
h² = 49/4
h = 7/2 ⇒ 3.5 cm
Then r = 2h
r = 2(3.5) ⇒ 7 cm
Volume of Cylinder = πr²h
= 22/7 × 7 × 7 × 3.5
= 539 cm³
:) Hope this Helps !!!
CSA = 1/3 × 462
CSA = 154 cm²
Then TSA of Cylinder = 2πr(r+h)
462 = 2πr(h+r) ......(1)
Also CSA of Cylinder = 2πrh
154 = 2πrh ......(2)
Dividing (1) and (2)
462/154 = 2πr(h+r)/2πrh
3 = (h+r)/h
3h = h+r
r = 2h ......(3)
Substituting (3) in (2)
154 = 2πrh
154 = 2 × 22/7 × 2h × h
2h² = 154 × 7/22 × 1/2
h² = 49/4
h = 7/2 ⇒ 3.5 cm
Then r = 2h
r = 2(3.5) ⇒ 7 cm
Volume of Cylinder = πr²h
= 22/7 × 7 × 7 × 3.5
= 539 cm³
:) Hope this Helps !!!
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