Question

A bucket of height $8cm$ made up of copper sheet is in the form of frustum of a right circular cone with radii of lower and upper ends as $3cm$ and $9cm$ respectively. Calculate:
i) the height of right circular cone

Answer 1

In $\Delta ADC$

$\tan \theta =\frac{AC}{9}$

In $\Delta BEC$

$\tan \theta =\frac{BC}{3}$

So $\frac{AC}{9}=\frac{BC}{3}$

$\Rightarrow 3(8+h)=9h$

$\Rightarrow 24+3h=9h$

$\Rightarrow 24=6h$

$\Rightarrow h=4cm$

$H=h+8$

$=12cm$.