Question 80

A right circular cylinder has its height two timesits radius. It is inscribed in a right circular cone having its diameter 10 cm and altitude 12 cm, and the axes of both the cylinder and cone coincide. The radius of the cylinder is

Solution

Let radius of cylinder = $$x$$ cm and its height = $$2x$$ cm

Height of cone = $$h=12$$ cm and radius of cone = $$r=5$$ cm

Since, the axes coincide, thus in the two similar triangles, we have : $$\frac{y}{h}=\frac{x}{r}$$

=> $$\frac{12-2x}{12}=\frac{x}{5}$$

=> $$60-10x=12x$$

=> $$12x+10x=22x=60$$

=> $$x=\frac{60}{22}=2\frac{8}{11}$$ cm

=> Ans - (A)

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