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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