Irving lives in appletown, and plans to drive along Highway 42, a straight highway that leads to Bananatown,
located 127 miles east and 20 miles north. Carol lives in
Cocnutville, located 94 miles east and 42 miles south of Appletow.
Highway 86 runs directl north from Coconutville, and junctions with
Highway 42 before heading further north to Durianville. Carol and
Irving are planning to meet up at park-and-ride at the junction of the
highways and carpool to Bananatown. Irving leaves Appletown at
8am, driving his usual 45 miles per hour. if Carol leaves
Coconutville at 9am, how fast will she need to drive to arrive at the
park-and-ride the same time as Irving?
SILVER
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ULRI
MURPLE
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on friday there were 15 birds

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.

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step-by-step explanation:

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i know the way

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