Question

♡LOTS OF POINTS TO RIGHT ANSWER♡

------Find the surface area of the figure, round your answer to the nearest hundredth if necessary <3
5.1 in
1 in​

Answer 1

`\approx19.16`

Explanation:

To find the surface area of a cone, one uses the following formula,

`A=(\pi)(r)(r+√(h^2+r^2)})`

Where (r) is the radius of the base of the cone, and (h) is the height of the cone, (
`\pi`) represents the numerical constant (3.1415...). In order for this formula to work, one needs the height of the cone. This can be found using the Pythagorean theorem. One can form a right triangle with the base's radius, the side length, and height of the cone, then solve for the height of the cone. The Pythagorean theorem states the following,

`a^2+b^2=c^2`

Substitute,

`a^2+(1)^2=(5.1)^2`

Simplify,

`a^2+1=26.01`

Inverse operations,

`a^2=25.01\\a\approx5`

Now one can use the formula to find the surface area of a cone, substitute in the given values, and solve,

`A=(\pi)(r)(r+√(h^2+r^2)})`

Substitute,

`A=(\pi)(1)(1+√(5^2+1^2)})`

`A=(\pi)(1+√(25+1))\\A=\pi(1+√(26))\\A\approx 19.16`