Question

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

Answer 1

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