Question 87

P, Q and R are the volumes of a cone, hemisphere and a cylinder with equal radius and height. What is the value of $$P : Q : R$$ ?

Solution

vol of cone : vpl of hemisphere : vol of cyclinder

$$\frac{1}{3}\times \pi\times r^2\times h$$ :$$\frac{2}{3}\times \pi\times r^3$$:$$\pi\times r^2\times h$$ = P:Q:R

having equal radius and height

$$\frac{1}{3}\times \pi\times r^2\times r$$ :$$\frac{2}{3}\times \pi\times r^3$$:$$\pi\times r^2\times r$$= P:Q:R

$$1 : 2 : 3$$

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