Question
Download Solution PDFThe ratio of radius and height of a cylinder is 5 ∶ 7 and its volume is 550 cm3. Calculate the curved surface area.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio of radius and height of a cylinder is 5 ∶ 7
Volume (V) = 550 cm3
Formula used:
Volume of a cylinder, V = πr2h
Curved Surface Area (CSA) = 2πrh
Calculation:
Let the radius (r) = 5k and height (h) = 7k
Volume, V = πr2h
⇒ 550 = π(5k)2(7k)
⇒ 550 = 22/7 × 25k2 × 7k
⇒ 550 = 550k3
⇒ k3 = 1
⇒ k = 1
Therefore, r = 5 × 1 = 5 cm and h = 7 × 1 = 7 cm
Curved Surface Area, CSA = 2πrh
⇒ CSA = 2 × 22/7 × 5 × 7
⇒ CSA = 220 cm2
∴ The correct answer is option (4).
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