Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine. The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 6:00 a. m. until 2:00 p. m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 6:30 a. m. and 11 a. m. The distribution of cookies is shown in the graph below.

2/5

step-by-step explanation:

answer: 2530

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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.