Question 129

The curved surface area and the total surface area of a cylinder are in the ratio 1:2 If the total surface area of the right cylinder is 616 cm , then its volume is :

Solution

Let radius of cylinder be $$r$$ and height be $$h$$

=> $$\frac{2 \pi rh}{2 \pi rh + 2 \pi r^2} = \frac{1}{2}$$

=> $$\frac{h}{h + r} = \frac{1}{2}$$

=> $$h = r$$

Total surface area = $$2 \pi rh + 2 \pi r^2 = 616$$

=> $$2 \pi r^2 + 2 \pi r^2 = 616$$

=> $$r^2 = \frac{154 * 7}{22}$$

=> $$r = 7 = h$$

Now, volume of cylinder = $$\pi r^2 h$$

= $$\frac{22}{7} * 7^2 * 7$$

= $$1078 cm^3$$

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