A solid cylinder has total surface area of 462 cm² is curved area is one third of its total surface area. Find the volume of cylinder [ take π = 22/7 ]
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Answer:
539 cm³
Step-by-step explanation:
(i)
Given that Total surface area of cylinder = 462 cm²
2πr(r + h) = 462 cm²
(ii)
Given that Curved surface area is (1/3)rd of its TSA.
⇒ 2πrh = (1/3) * 462
⇒ 2πrh = 154 cm²
On solving (i) ÷ (ii), we get
⇒ [2πr(r + h)/2πrh] = 462/154
⇒ (r + h)/h = 3
⇒ r + h = 3h
⇒ r = 2h
⇒ h = r/2 ---- (iv)
Substitute h = r/2 in (ii), we get
⇒ 2πrh = 154
⇒ πr² = 154
⇒ (22/7) * r² = 154
⇒ r² = 49
⇒ r = 7 cm
Substitute r = 7 in (iv), we get
⇒ h = r/2
⇒ h = 7/2
⇒ h = 3.5 cm
Volume of cylinder = πr²h
= (22/7) * (7)² * 3.5
= 539 cm³
Therefore, Volume of cylinder = 539 cm³.
Hope it helps!
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Heya ..❤❤❤✔✔✔✔
539cm^3✔✔✔✔
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