Question

ASAP please help I’m failing math

Answer 1

Part A) The volume of the entire cone is
`168\pi\ in^3`

Part B) see the explanation

Explanation:

Part A) we know that

The volume of a cone is equal to

`V=(1)/(3)\pi r^(2)h`

where

r is the radius of the base of the cone

h is the height of the cone

In this problem triangle ABD is similar to triangle ACE

Remember that If two figures are similar, then the ratio of its corresponding sides is proportional

so

`(AB)/(AC)=(BD)/(CE)`

substitute the given values

`(7)/(14)=(3)/(x)`

solve for x

`x=14(3)/7\\x=6\ in`

To find out the volume of the entire cone we have

`r=CE=x=6\ in`

`h=AC=14\ in`

substitute in the formula

`V=(1)/(3)\pi (6)^(2)(14)`

`V=168\pi\ in^3`

Part B) How did you determine the value for x in triangle ACE

In this problem triangle ABD is similar to triangle ACE

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

`(AB)/(AC)=(BD)/(CE)`

substitute the given values and solve for x