Question

How to solve for problem 21? Calculate the surface area of the hemisphere with the knowledge that the circumference of a great circle is 40.8 inches.

Answer 1

In order to get the surface area of a hemisphere, let's determine its radius first.

Based on the question, the circumference of a great circle is 40.8 inches. Since circumference = 2πr, then 40.8 inches = 2πr. From this, we can solve for the radius.

`40.8=2\pi r`

To solve for the radius, divide both sides of the equation by 2π. Use π = 3.14159

`(40.8)/(2\pi)=r`
`(40.8)/(2(3.14159))\Rightarrow(40.8)/(6.28318)\Rightarrow6.4935`

Therefore, the length of the radius is 6.4935 inches.

Now that we have the radius, let's calculate the surface area of the hemisphere. The formula is:

`SA_(hemisphere)=3\pi r^2`

Let's plug into the formula r = 6.4935 inches and π = 3.14159

`SA_(hemisphere)=3(3.14159)(6.4935in)^2`

Then, solve.

`SA_(hemisphere)=(9.42477)(42.1655in^2)`
`SA_(hemisphere)\approx397.4in^2`

Therefore, the surface area of the hemisphere is approximately 397.4 square inches.