Given: line a b intersects line d e at point c. prove: angledcb is-congruent-toangleeca line d e intersects line b a at point c. a 2-column table with 6 rows. column 1 is labeled statements with the entries line a b intersects line d e at point c, angle d c b and angle b c e are a linear pair, angle d c b is supplementary to angle b c e, angle b c e and angle e c a are a linear pair, angle b c e is supplementary to angle e c a, angle d c b is-congruent-to angle e c a. column 2 is labeled reasons with the entries given, definition of linear pair, linear pair post, definition of linear pair, question mark, congruent to supplementary theorem. what is the missing reason in step 5? linear pair postulate given definition of complementary angles congruent complements theorem

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the awnser is visionary