Answer:
90•pi aka 90pi
Explanation:
Okay, so first is first the formule for finding the surface area of a cone is, Surface Area=pi•r^2+pi•radius•slant height. The question here states that the surface area is B+pi•r•slant height. I replace B with pi•r^2 since that is the area of a circle. A cone has a circle for a base, and we can use the formula of a circle for base. To make things clear, “^” is what I used to show exponents, and “•” is what I use as a multiplication sign. R stands for radius.Now, the question says to leave the answer in terms of pi. That means we do not use pi while finding the surface area. We can remove pi from the equation, Surface Area= r^2+radius•slant height. Radius is 5 because that is half of the diameter (diameter is half circle), and we are given 12 as the height. Even though we were given the height of the cone, we need the slant height to find the surface area with the equation we were given. By looking at the picture, we can see a right triangle. 12 is the height, it is a side of the right triangle, and 5 is the radius, it is a side of the right triangle. The hypotenuse is the unknown side, and is the slant height of the cone. We can use the pythagorean theorem for finding the unknown side length. The pythagorean theorem is c^2=a^2+b^2. C is the hypotenuse, and a and b are the other side lengths of the right triangle. Just a reminder, pythagorean theorem only works for right triangles. By plugging in the values, c^2=12^2+5^2, 12•12=144, 5•5=25, and 144+25=169. c^2=169, left with 2 as an exponent for the unknown number, we can use inverse operations to isolate for c. Opposite of exponent is square rooting, so c= The square root of 169. I use desmos scientific calculator for finding the square root of 169. 13 is what c is equal too, meaning that 13 is the slant height. Having the slant height allows us to solve for the surface area of the cone now. Surface Area= 5^2+5•13, when solved is equal to 90. In terms of pi, we did not need to multiply pi with the answer, so we just put pi next to it. 90pi is the answer I got. If incorrect I am sorry, and I hope this answer helps Have a great day