To solve this problem, we have to get the data in the question and then substitute the values into the formula and solve.
The lateral surface area of the cone is 640.874in^2.
Lateral Surface Area
Lateral surface area of an object is the sum of the total areas of the object.
The formula of lateral surface area of a cone is given as
[tex]A = 2\pi rh[/tex]
Let's substitute the values into the equation and solve.
- diameter = 13in,
- radius = 13/2 = 6.5in
- slant height = 17in
Using Pythagora's theorem, we can find the height of the cone
[tex]17^2 = 6.5^2 + h^2\\h^2 = 17^2 - 6.5^2\\h^2 = 246.75\\h = \sqrt{246.75} \\h = 15.70[/tex]
Substituting the values into the formula, we can solve for the lateral surface area
[tex]A = 2\pi rh\\A = 2 * 31.14 * 6.5 8 15.70\\A = 640.874in^2[/tex]
The lateral surface area of the cone is 640.874in^2
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