Formula for the volume of cone is [tex] \frac{1}{3} \pi r^2h [/tex]
Where r= radius of the cone
h = height of the cone
The value of pi is 3.14
Given volume of larger cone is 131 cm^3
Volume of larger cone = [tex] \frac{1}{3} \pi r^2h [/tex]
131 = [tex] \frac{1}{3} \pi 5^2h [/tex]
Solve for h
131 = 26.1667 *h
So h= 5 cm
The height of bigger cone = 5cm
Now we find the volume of smaller cone
Two cones similar so the sides are in proportional
[tex] \frac{radius(small)}{radius(large)}= \frac{height(small)}{height(large)} [/tex]
[tex] \frac{2}{5} =\frac{ height of small}{5} [/tex]
Height of smaller cone = 2cm
volume of smaller cone = [tex] \frac{1}{3} \pi 2^2*2 [/tex]
= 8.38cm^3
