Find the slant height of a cone with surface area of 178.6 in2 and a radius of the base of 4.9 in
a = pi r s
178.6 = 3.14 * 4.9 * s
s = 11.6
or, if you are including the base of the cone,
a = pi*r(r+s)
178.6 = 3.14 * 4.9 (4.9+s)
s = 6.71
To find the slant height of a cone, we can use the formula:
slant height = √(radius^2 + height^2)
Given the surface area of the cone and the radius of the base, we need to find the height of the cone in order to calculate the slant height. Let's break down the problem into steps:
1. We know that the surface area of a cone is given by the formula:
surface area = π * radius * (radius + slant height)
Substituting the given values, we have:
178.6 in^2 = π * 4.9 in * (4.9 in + slant height)
2. Rearrange the equation to solve for the slant height:
178.6 in^2 / (π * 4.9 in) = (4.9 in + slant height)
Now, we have an equation to solve for the slant height:
178.6 in^2 / (π * 4.9 in) - 4.9 in = slant height
3. Use a calculator to evaluate the right side of the equation:
slant height ≈ 6.129 in
Therefore, the slant height of the cone is approximately 6.129 inches.