Pls help A right circular cone has a lateral surface area of 188.50 square inches. If its slant height lis 10 inches, then what is the volume of the cone in cubic inches?

169.04 in² (nearest hundredth)

Step-by-step explanation:

Surface area of a cone = r² + r

(where r = radius of the base and = slant height)

Given slant height = 10 and surface area = 188.5

Surface area  = r² + r

188.5 = r² + 10r

r² + 10r - 188.5 = 0

r = = 4.219621117...

Volume of a cone = (1/3)r²h

(where r = radius of the base and h = height)

We need to find an expression for h in terms of using Pythagoras' Theorem a² + b² = c², where a = radius, b = height and c = slant height

r² + h² = ²

h² = ² - r²

h = √(² - r²)

Therefore, substituting found expression for h:

volume of a cone = (1/3)r²√(² - r²)

Given slant height = 10 and r = 4.219621117...

volume = 169.0431969... = 169.04 in² (nearest hundredth)

Check the picture below.

notice, the slant-height is simply the hypotenuse from the pythagorean theorem.

1010: 3030

is it i think