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.