Question

Please give a step by step explanation for this question

Answer 1

`108\pi` or approx.
`339.3 m^(2)`

Explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere,
`SA_(tot) =4\pi r^2`. But we need it for a hemisphere, so multiply the equation by
`(1)/(2)`.

`SA} = ((1)/(2)) 4\pi r^2` =>
`SA} =2\pi r^(2)`

We also need the area of the base, which is circle.
`A_(circle)=\pi r^(2)`.

Now add these equations together to get our equation.

`SA_(tot) =2\pi r^2 +\pi r^(2)` =>
`SA_(tot) =3\pi r^2`

Now we have the proper equation for total surface area of a hemisphere,
`SA_(tot) =3\pi r^(2)`. Plug in the value of
`r` which is given in the problem,
`r=6m`.

=>
`SA_(tot) =3\pi (6)^(2)` =>
`SA_(tot) =3\pi (36)` =>
`SA_(tot) =108\pi m^(2)` or approx.
`339.3 m^(2)`