in the June 2003 GCSE higher maths paper, a question asks ' a thin-walled glass paperweight consists of a hollow cylinder with a hollow cone on top as shown. the paperweight contains just enough sand to fill the cylinder' i need to calculate the depth. could you provide the working out for the answer, please
in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Best answer

If the length of the cylinder is c and the radius of the cone and cylinder is r, and the height of the cone is h, the volume of the cylinder is πr^2c (which is also the volume of sand), and the volume of the cone is πr^2h/3. The combined volume is πr^2(c+h/3).

If the sand is used to fill the cone first the surplus of sand will be πr^2c-πr^2h/3=πr^2(c-h/3).

This surplus is used to part fill the cylinder to a depth of x, so that πr^2x=πr^2(c-h/3) and x=c-h/3.

There is no more information or picture to put values for c or h, but if c=h x=2h/3 or 2c/3, that is, two thirds the height of the cone or cylinder.

by Top Rated User (1.1m points)

Related questions

1 answer
asked May 2, 2018 in Other Math Topics by Reema Level 1 User (200 points) | 373 views
1 answer
asked Sep 29, 2013 in Word Problem Answers by helpmepls Level 1 User (120 points) | 917 views
1 answer
asked Jul 13, 2013 in Statistics Answers by Leon89 Level 1 User (160 points) | 1.6k views
1 answer
1 answer
1 answer
asked Sep 14, 2017 in Algebra 1 Answers by s-factor Level 1 User (160 points) | 360 views
1 answer
asked Oct 1, 2014 in Other Math Topics by VYSAKH PA Level 1 User (260 points) | 1.1k views
1 answer
1 answer
asked Nov 17, 2013 in Other Math Topics by Edd Level 2 User (1.3k points) | 687 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,542 questions
99,804 answers
2,417 comments
523,077 users