Question

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

Answer 1

`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`

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`