Question

AREAS AND VOLUMES OF SIMILAR SOLIDS URGENT?

Answer 1

Formula for the volume of cone is
`(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 =
`(1)/(3) \pi r^2h`

131 =
`(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

`(radius(small))/(radius(large))= (height(small))/(height(large))`

`(2)/(5) =( height of small)/(5)`

Height of smaller cone = 2cm

volume of smaller cone =
`(1)/(3) \pi 2^2*2`

= 8.38cm^3