Question

The question is embedded on the first image. On the second image are the answer choices needed for the blank rectangles.

Answer 1

Given the function

`y=(1)/(4)x`

the vertical line is given by the point

( x , 0 )

the area of the triangle is

`At=(b*h)/(2)`

where

base= value of x

height=value of y

then

the expression of the area as a function of x is

`At=(x*(1)/(4)x)/(2)`
`At(x)=(x^2)/(8)`

Then when x=5

`At(5)=(5^2)/(8)`
`At(5)=(25)/(8)=3.125un^2`

The volume of the cone is given by

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

where

h= value of x

r= value of y

then the volume of the cone as a function of x is

`Vc=(1)/(3)\pi *((1)/(4)x)^2*x`
`Vc=(\pi x^3)/(3*4^2)`
`Vc(x)=(\pi x^3)/(48)`

The volume of the cone when x=16 is

`Vc(16)=(\pi(16)^3)/(48)`
`Vc(16)=(256\pi)/(3)`
`Vc(16)=(256\pi)/(3)=268.082un^3`