When broken open Austen's jawbreaker will make a hemisphere.
Recall that the total surface area of a hemisphere is given by
[tex]TSA=3\pi r^2[/tex]
Where r is the radius of the hemisphere.
We are given the diameter of the hemisphere that is 16.4 inches.
The radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{16.4}{2}=8.2\: in[/tex]
So, the radius is 8.2 inches
Substitute the radius into the above formula of total surface area
[tex]TSA=3\pi r^2=3\pi(8.2)^2=3\pi(67.24)=633.72\: in^2[/tex]
Therefore, the total surface area of the hemisphere is 633.72 square inches.
Please note that if you want to find out only the curved surface area then use the following formula
[tex]CSA=2\pi r^2=2\pi(8.2)^2=453.96\: in^2[/tex]
For the given case, the curved surface area is 453.96 square inches.
