Nathan weighs 12 more pounds than Marty.
If Marty weighs 64 pounds and Nathan weighs 76 pounds, we can subtract the weight of Marty from Nathan to get our answer.
In case Nathan was actually 476 pounds, the answer would be 412.
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.
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.
76 pounds. How much more does Nathan wei...