Question
Download Solution PDFThe radius and height of a cylinder are in the ratio 6 : 7 and its volume is 792 cm3. Calculate its curved surface area in cm2.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio of the radius to the height of the cylinder = 6 : 7
Volume of the cylinder = 792 cm³
Formula used:
Volume of a cylinder = πr²h
Curved surface area of a cylinder = 2πrh
Calculation:
Let the common ratio be x.
Then, the radius r = 6x and the height h = 7x.
Using the volume formula:
π(6x)²(7x) = 792
⇒ π × 36x² × 7x = 792
⇒ 252πx³ = 792
Take π as 22/7:
⇒ 252 × 22/7 × x³ = 792
⇒ 792x³ = 792
⇒ x³ = 1
⇒ x = 1
Thus, radius r = 6x = 6 × 1 = 6 cm
And height h = 7x = 7 × 1 = 7 cm
Now, calculate the curved surface area:
Curved surface area = 2πrh = 2 × 22/7 × 6 × 7
= 2 × 22 × 6
= 264 cm²
∴ The curved surface area of the cylinder is 264 cm².
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