How to Calculate the Surface Area of cone with radius of 1.8cm and height of 2.4cm?

1 Answer
Mar 1, 2018

27.1296 cm^2

Explanation:

The formula for the surface area of a cone is Sa = pirl + pir^2
Sa = surface area
r = radius
l = slant height
From the given information, we already have some of the numbers. We know that
r = 1.8 cm
pi = 3.14
h = 2.4 cm
However, we do not know the slant height of the triangle. Using this picture below as a guide, you can fill in r and h
enter image source here
Using the Pythagorean Theorem (a^2 + b^2 = c^2), we can find l

We can say that h^2 + r^2 = l^2 by using substitution. So lets plug the numbers into this equation.
2.4^2 + 1.8^2 = l^2
5.76 + 3.24 = l^2
9 = l^2
sqrt9 = l
3 = l

Yay! We've solved the first part. Now that we know all our variables, we can plug that into the first equation.
Sa = pirl + pir^2
Sa = 3.14(1.8)(3) + 3.14(1.8^2)
Sa = 16.956 + 10.1736
Sa = 27.1296cm^2