Question

♡LOTS OF POINTS TO RIGHT ANSWER♡

Answer 1

Answer:

$\approx19.16$

Step-by-step explanation:

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

$A=(\pi)(r)(r+\sqrt{h^2+r^2}})$

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,

$A=(\pi)(r)(r+\sqrt{h^2+r^2}})$

Substitute,

$A=(\pi)(1)(1+\sqrt{5^2+1^2}})$

$A=(\pi)(1+\sqrt{25+1})\\A=\pi(1+\sqrt{26})\\A\approx 19.16$