Question

The cone shown has a radius of 5 feet and a slant height of 12 feet. Which choice is closest to the total surface area? Use 3.14 to approximate pi.
60 square feet


79 square feet


188 square feet


267 square feet

Answer 1

So first of all, to solve this, we need to know the formula for finding the surface area of a cone. The formula is :
$SA = \pi r(r+ \sqrt{ h^{2} + r^{2} } )$
Where SA stands for surface area, h stands for height, and r stands for radius.
In the given information, we are not told the height, but we are told the slant height.

In a cone, the slant height, the height, and the radius together form a right triangle. We can use that triangle to solve for the height
So, to find the height, we can do:

5^2+b^2 = 12^2, or 25+b^2 = 144
Therefore, b is equal to about 11

So now, we can plug all of our values into the formula
This gives us:
$SA = \pi * 5 (5+ \sqrt{ 5^{2} + 11^{2} } )$

If we solve, this gives us about 267. 

Therefore the answer is 267 feet squared

Hope this helped!! :D

Answer 2

Sa=π•r(r+√h²+r²
sa=π•r²+r•√h²+r²
sa=3.14•5²+5•√11²+5²
sa=78.5+5•12.08
sa=267