Question

A. 5/7 pi B. 4/9 pi C. 6/7 pi D. 2/3 pi E. 5/9 pi

Answer 1

Answer:

A. 2.243994753

B. 1.396263402

C. 2.692793703

D. 2.094395102

E. 1.745329252

Answer 2

Answer:

D

Step-by-step 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