Question

the height of cone is 13 cm is a small cone is cut of at the top by a plane parallel to the base . if its volume is 1/27 of the volume of the given cone at what height is the base is the section board

Answer 1

$\text{height of big cone is 13 cm}$
$\text{Let the height of small cone is h}$
$\text{A/C to question,}$
$\frac{\text{volume of big cone} }{27}= \text{volume of small cone}$
$\text{so,}\\\frac{\pi\times R^2\times H}{3\times27}=\frac{\pi\times r^2\times h}{3}$
$\frac{H}{h}=\frac{27r^2}{R^2}$
$\text{now,}$
$\text{we see that two triangles are similar so, }$
$\frac{H}{h}=\frac{R}{r}$
$\text{hence,}\\\frac{H^3}{h^3}=\frac{27}{1}$
H/h = 3/1
h = H/3 = 13/3 cm
hence, height of small cone is 4.33 cm
so, height of second board = H - H/3
= 2H/3cm
= 26/3 cm
= 8.667 cm