Answer:
360π in²
Explanation:
SA = πrl + πr²
π = pi
r = radius = 10
l = lateral height = 26
h = height = x
To find the height, we will need to set up an equation. As you can see, the height, radius, and lateral height come together to form a right triangle, so we can use the Pythagorean Theorem to find x.
a² + b² = c²
10² + x² = 26²
x² + 100 = 676
x² + 100 - 100 = 676 - 100
x² = 576
√x² = √576
x = 24
The height of the cone is 24 in. Now we can input all of these values into the above equation and solve for SA.
SA = πrl + πr²
SA = π(10)(26) + π(10²)
SA = 260π + 100π
SA = 360π
The total surface area of the cone is 360π in².
Hope this helps!