Find the radius of a right cone with slant height 21 m and surface area 168pi m2

Does that surface area include the base?

The area of the conical portion is
A = pi* R * (slant height)

You can use that formula to solve for the radius, R

See http://www.uwm.edu/~ericskey/TANOTES/Geometry/node15.html

To find the radius of a right cone, we need to use the formula for the surface area of a cone, which is given by:

Surface Area = πr(r + l)

where r is the radius and l is the slant height.

In this case, the surface area is given as 168π m² and the slant height is given as 21 m. So we can rewrite the formula as:

168π = πr(r + 21)

Let's solve this equation step by step to find the value of r.

First, divide both sides of the equation by π:

168 = r(r + 21)

Now, let's expand the equation:

168 = r² + 21r

Next, move all the terms to one side to create a quadratic equation:

r² + 21r - 168 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula here:

r = (-b ± √(b² - 4ac)) / (2a)

In this equation, a, b, and c represent the coefficients of the quadratic equation:

a = 1, b = 21, c = -168

Substituting these values into the quadratic formula, we get:

r = (-21 ± √(21² - 4(1)(-168))) / (2(1))

Simplifying further:

r = (-21 ± √(441 + 672)) / 2

r = (-21 ± √(1113)) / 2

Now, we have two possible values for r. Let's calculate both:

r₁ = (-21 + √(1113)) / 2

r₂ = (-21 - √(1113)) / 2

Calculating these values using a calculator, we find:

r₁ ≈ 4.42 m
r₂ ≈ -25.42 m

The radius of a cone cannot be negative, so the radius of the right cone is approximately 4.42 m.