Avideo game designer places an anthill at the origin of a coordinate plane. a red ant leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the anthill and moves along a straight line to (? 1, ? 1). next, the red ant moves to (2, 2), while the black ant moves to (? 2, ? 2). then the red ant moves to (3, 3), while the black ant moves to (? 3, ? 3), and so on. complete the explanation of why the red ant and the black ant are always the same distance from the anthill. at any given moment, the red ant's coordinates may be written as (a, a) where a > 0. the red ant's distance from the anthill is . the black ant's coordinates may be written as (? a, ? a) and the black ant's distance from the anthill is . this shows that at any given moment, both ants are units from the anthill.

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.

17.08

correct me if i am wrong.

step-by-step explanation: hi!