Answer:
D
Explanation:
Remark
This is an incredibly beautiful problem! It is solved mostly by algebra. r = 1 and the height will therefore be 2
Equations
l^2 + r^2 = l^2
l is the slant height.
Solution
SA = π * l * r + π r² = π(1 + √5) Divide both sides by π
Find l
l * r + r^2 = 1 + √5
l^2 = r^2 + h^2
l^2 = r^2 + (2r)^2
l^2 = 5r^2
l = √5 * r
Now go back to this equation to find r
l * r + r^2 = 1 + √5 Substitute the value for l
√5 r * r + r^2 = 1 + √5 On the left pull out r^2
r^2 (1 + √5) = 1 + √5 Divide by 1 + √5
r^2 = 1 Take the square root on both sides
sqrt(r^2) = sqrt(1)
r =1
Therefore h = 2
Volume of the cone.
V = 1/3 * π r² h
V = 1/3 * π 1² 2
V = 2/3 * pi
D