Which is the best strategy to use to solve this problem?
mr. jackson wants to build a pool in his backyard. he plans to put a safety fence around the rectangular pool area that has an area of 400 square feet. he wants to use as little fence material as possible.
what are the dimensions mr. jackson should use for his rectangular pool area?
a.
make a list.
create a list of all possible whole-number combinations of length and width that would equal an area of 400 square feet. then start calculating the perimeter of each rectangle. look for a pattern to decrease the number of calculations you have to make.
b.
write a number sentence.
use a number sentence to calculate the area of a rectangle. use guess and check to find two numbers that when multiplied will give a product of 400.
c.
use objects.
arrange 400 square tiles in different patterns until you get a rectangular shape. count the number of tiles on the perimeter of the shape.

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.