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Question

The ratio between the radius of the base and the height of cylindrical is $$2:3$$. Find the total surface area of the cylinder, if its volume is $$1617\ { cm }^{ 3 }$$  


Solution

Let $$r=2x$$ and $$h=3x.$$

$$V=\pi r^2 h$$

$$\implies \dfrac{22}{7}\times (4x^2)(3x)=1617$$

$$\implies x^3=42.875$$

$$\implies x=3.5cm$$

Hence, $$r=7cm$$ and $$h=10.5cm$$

Total surface area$$=2\pi rh+2\pi r^2=2\pi r(r+h)$$

$$=2\times \dfrac{22}{7}\times 7(17.5)$$

$$=770cm^2$$

Mathematics

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