# Thread: Finding the Surface Area of a Cone?

1. ## Finding the Surface Area of a Cone?

I am reviewing for the 11th grade state assessment tests which are coming up soon. The formula I am given for finding the surface area of a cone is:

SA = πr² + πr √r² + h²

The information I am given in the example problem is: r = 3 cm, h = 4 cm.

----------
I am not here to ask for the answer - I simply wonder what to do next. My work so far looks like this:

SA = πr² + πr √r² + h²
SA = π(3²) + π(3) √(3²) + (4²)
SA = 37.699 √25

The correct answer in this question is given: 75.36 sq cm. Did I do my order of operations wrong (for what I have shown), and, how do you find the final answer?

Any help is appreciated, thank you.

2. Originally Posted by AlderDragon
I am reviewing for the 11th grade state assessment tests which are coming up soon. The formula I am given for finding the surface area of a cone is:

SA = πr² + πr √r² + h²

The information I am given in the example problem is: r = 3 cm, h = 4 cm.

----------
I am not here to ask for the answer - I simply wonder what to do next. My work so far looks like this:

SA = πr² + πr √r² + h²
SA = π(3²) + π(3) √(3²) + (4²)
SA = 37.699 √25

The correct answer in this question is given: 75.36 sq cm. Did I do my order of operations wrong (for what I have shown), and, how do you find the final answer?

Any help is appreciated, thank you.
Hi AlderDragon,

$\displaystyle S.A.=\pi r^2+\pi r \sqrt{r^2+h^2}$

$\displaystyle S.A.=\pi \cdot 3^2 + 3\pi \sqrt{3^2+4^2}$

$\displaystyle S.A.=\pi \cdot 9 + 3\pi \sqrt{25}$

$\displaystyle S.A.=9 \pi + 15 \pi$

$\displaystyle S.A. \approx 75.4 \,cm^2$