Question

AREAS AND VOLUMES OF SIMILAR SOLIDS URGENT?

Answer 1

Formula for the volume of cone is $\frac{1}{3} \pi r^2h$

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 = $\frac{1}{3} \pi r^2h$

131 = $\frac{1}{3} \pi 5^2h$

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

$\frac{radius(small)}{radius(large)}= \frac{height(small)}{height(large)}$

$\frac{2}{5} =\frac{ height of small}{5}$

Height of smaller cone = 2cm

volume of smaller cone = $\frac{1}{3} \pi 2^2*2$

= 8.38cm^3