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  • A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8: 5, show that the ratio between the radius of their bases to their height is 3: 4.    

A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8: 5, show that the ratio between the radius of their bases to their height is 3: 4.  

 

Answers (1)

Let radius be r and height be h 

\frac{2\pi rh}{\pi r l } = \frac{8}{5}\\\\ 5 h = 4 l \\\\ 5 h = 4 \sqrt { h ^2 + r ^2 } \\\\ 25 h ^2 = 16 ( h ^2 + r ^2 ) \\\\ 25 h ^ 2 = 16 h ^2 + 16 r^2 \\\\ 9 h^ 2 = 16 r^2

\frac{h^2 }{ r^2 } = \frac{16}{9}\\\\ \frac{r}{h} = \frac{3}{4}

It is proved that the ratio between the radius of their bases to their height is 3: 4 

Posted by

Safeer PP

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