Question 113

The sum of the radius and height of a cylinder is 42 cm. Its total surface area is 3696 cm 2. What is the volume of cylinder ?

Solution

Total surface area of cylinder

=> $$2 \pi r h + 2 \pi r^2 = 3696$$

=> $$2 \pi r (r + h) = 3696$$

$$\because (r + h) = 42$$ [Given]

=> $$2 \times \frac{22}{7} \times r \times 42 = 3696$$

=> $$44 \times 6 \times r = 3696$$

=> $$r = \frac{3696}{44 \times 6} = 14$$ cm

=> $$h = 42 - 14 = 28$$ cm

$$\therefore$$ Volume of cylinder = $$\pi r^2 h$$

= $$\frac{22}{7} \times 14 \times 14 \times 28$$

= $$17248 cm^3$$

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