Question

6. A cone has a base area of 36 cm². A parallel slice5 cm from the vertex has an area of 25 cm?. Findthe height of the cone.

Answer 1

The given situation is modeled by the following formula

$A_{\text{vertex}}=r^2\cdot A_{base}$

Where r = 5/h, then

$\begin{gathered} 25=(\frac{5}{h})^2\cdot36 \\ 25=\frac{25}{h^2}\cdot36 \\ h^2=\frac{25}{25}\cdot36 \\ h=\sqrt[]{36} \\ h=6 \end{gathered}$

Hence, the height of the cone is 6 centimeters.