Praxis Core Math

Question

Picture an ice cream cone filled part way with water. The text for the question is below, as well as my (incorrect) solution. Can anyone help me figur out where I went wrong. Unfortunately the answer is not given for this one as it is taken from an ETS practice exam purchased online.

 

QUESTION

The figure above shows a right circular cone with base radius 6 and height 20. The shaded portion of the figure is a right circular cone with height 10. The volume of the smaller cone is what fraction of the volume of the larger cone?
(The volume of a right circular cone with base radius r and height h is 1/3 pieR3H)

 

MY SOLUTION (incorrect)

 

Large cone= 1/3 x pie x 6² x 20 = (720 x pie)/3 = 240 x pie = 753.982

 

Small cone = 1/3 x pie x 3² x 10 = 1/3 x pie x 90= (90 x pie)/3 = 94.25

 

94/754 = 12/100

 

 

 

Answer 1

Actually you have the right answer, which is 1/8.  If you don't round you'll see that 753.982/94.25 = 7.99999 or 8.  So invert that and you get 1/8.  But you didn't need to multiply out the pis or the (1/3)s because when you take the ratio they cancel, leaving you with:

 

V_S/V_L = 3²/(6²·2) = 9/72 = 1/8

 

Now the way most tutors would do it.  The large cone has a base radius of 6 and a height of 20.  The small cone has a base radius of 3 and a height of 10.  The two cones are similar with a scale factor (small cone/large cone) of 1/2.  The ratio of their surface areas will be (1/2)² = 1/4 and the ratio of their volumes will be (1/2)³ = 1/8.