Jade scooped sand from a completely filled cylinder using cone shaped container. The Cylinder had a diameter of 12 inches and a height of 5 inches, and was one-fourth full after she scooped one full scoop of sand. What were the dimensions of the cone shaped container? Use 3.14 to approximate pi.

A. h=5in; r = 9in

B. h = 9.6; r = 15 in

C. h = 11.25 in; r = 12 in

D. h = 15 in; r = 6 in

Volume of a Cylinder = pi * radius * radius * height

radius = diameter / 2 = 12 / 2 = 6

height = 5

so Volume of this Cylinder = 6*6*5 pi = 180 pi

one fourth full after being scooped

so Volume of Cone = (1 - 1/4) * Volume of Cylinder

= 3/4 * Volume of Cylinder = 3/4 * 180 pi = 135 pi

so Volume of this Cone = 135 pi

equation for Volume of Cone = (1/3) * radius * radius * height * pi

we set this equal to the value you just got

135 pi = (1/3) * radius * radius * height * pi

you can cancel pi from both sides

and multiply both sides by 3

(radius * radius * height) = 405

now let's see which options fit this!

A. 9 * 9 * 5 = 405

B. 15 * 15 * 9.6 = 2160

C. 12 * 12 * 11.25 = 1620

D. 6 * 6 * 15 = 540

So the only one that matches is A