Let's call the radius of the cone "r" and the height "h". We are given that the surface area of the cone is 250 square centimeters, so we can set up the equation for the surface area of a cone:
πr(r + √(r^2 + h^2)) = 250
We are also given that the height of the cone is double the length of its radius, so we can set up another equation:
h = 2r
Substituting h = 2r into the equation for the surface area of the cone and simplifying, we have:
πr(r + √(r^2 + (2r)^2)) = 250
πr(r + √(r^2 + 4r^2)) = 250
πr(r + √(5r^2)) = 250
πr(r + r√5) = 250
πr(2r + r√5) = 250
πr^2(2 + √5) = 250
r^2(2 + √5) = 250 / π
r^2 = 250 / (π(2 + √5))
r^2 ≈ 250 / (3.14(2 + 2.24))
r^2 ≈ 250 / (3.14 * 4.24)
r^2 ≈ 250 / 13.4828
r^2 ≈ 18.5576
r ≈ √18.5576
r ≈ 4.309
Since the question asks for the height of the cone to the nearest centimeter, and we are given that the height is double the length of the radius, the height is approximately 8 centimeters.
Therefore, the correct answer is:
A. 5 centimeters.
The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
A.5 centimeters
B.20 centimeters
C.15 centimeters
D.10 centimeters
1 answer
1 answer