The box plot compares Marta’s and Ani’s diving scores in the first several meets of the season. A number line goes from 0 to 12. Marta's whiskers range from 4 to 10, and the box ranges from 5 to 8. A line divides the box at 6. Ani's whiskers range from 4.5 to 9.5, and the box ranges from 6 to 9. A line divides the box at 8.
Based on the data in the box plots, what is the best evidence to show which diver had greater overall success during the meets so far this season?

Ani was more successful because she had an outlier.
Marta was more successful because she received the highest score.
Ani was more successful because she had the greater measure of center.
Marta was more successful because she had the greater total spread.

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.