When a concrete structure is built, an engineer often performs a slump test on the concrete to ensure that it is of suitable strength and consistency. The engineer fills a truncated cone with a bottom diameter 200mm, top diameter 100mm and height 300mm with concrete. The engineer then places the cone on the ground and lifts off the cone. After period of time, she measures the amount of that the top of the cone has slumped to decide if the concrete is appropriate.

Question

a) Original cone from which the slump test cone was derived had the height of 600m. What was the volume of the original cone? Express your answer to nearest cubic mm.

Formula to figure out the volume of the cone is -->V= 1/3ð<r2>h

This would have been quite easy if they had only given one diameter, but they have given two and I do not know which one to use. The top or bottom?

Also this is part b)

What was the volume of the slump-test cone?

Is it only the height which changes in this part. Because in the first part it was 600 and now it is 300 right? I am still unsure of which diameter to use, because there are 2.

Answer 1

this is the 6th time I have seen this problem

I think I answered it at
http://www.jiskha.com/display.cgi?id=1285717196

the other questions are at
http://www.jiskha.com/search/index.cgi?query=slump+test

Answer 2

I don't get how you found the solution. Also I am the first one to post part b) and I don't get how to do it.

Answer 3

visualize a cone of height 600 mm and a base diameter of 200 mm
Now slice it horizontally half-way up its height, the top part would be a cone of height 300 and diameter 100,
the bottom part a "truncated" cone with a base diameter 200 and top diameter 100

(If you have been to a circus, often they have elephants standing on solids like that)

So take the volume of the original cone
Vol = (1/3)π(100^2)(600)

Volume of small cone cut off
= (1/3)π(50^2)(300)

subtract to bet the volume of the truncated part.