Question

Determine the value of g(4), g(3 / 2), g (2c) and g(c+3) then simplify as much as possible.

g(r) = 2
`\pi` r h

Answer 1

For this case we have the following function:

`g (r) = 2 \pi * r * h`

We must evaluate the function for different values:

`g (4) = 2 \pi * (4) * h = 8 \pi*h\\g (\frac {3} {2}) = 2 \pi * (\frac {3} {2}) * h = 3 \pi*h\\g (2c) = 2 \pi * (2c) * h = 4 \pi * c * h\\g (c + 3) = 2 \pi * (c + 3) * h = 2 \pi * c * h + 6 \pi * h`

Answer:

`g (4) = 8 \pi*h\\g (\frac {3} {2}) =3 \pi*h\\g (2c) = 4 \pi * c * h\\g (c + 3) = 2 \pi * c * h + 6 \pi * h`

Answer 2

`g(4) = 8 \pi h\\\\g((3)/(2)) = 3 \pi h\\\\ g(2c) = 4 \pi ch\\\\g(c+3) = 2 \pi hc+6\pi h`

Explanation:

You need to substitute
`r=4` into
`g(r) = 2 \pi r h`. Then:

`g(4) = 2 \pi(4)h\\\\g(4) = 8 \pi h`

Substitute
`r=(3)/(2)` into
`g(r) = 2 \pi r h`. Then:

`g((3)/(2)) = 2 \pi((3)/(2))h\\\\g((3)/(2)) = 3 \pi h`

Substitute
`r=2c` into
`g(r) = 2 \pi r h`. Then:

`g(2c) = 2 \pi(2c))h\\\\g(2c) = 4 \pi ch`

Substitute
`r=c+3` into
`g(r) = 2 \pi r h`. Then:

`g(c+3) = 2 \pi (c+3)h\\\\g(c+3) = 2 \pi hc+6\pi h`