Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If the height of a cone is decreased by 20% whereas its radius is increased by 25% , can we find the percentage increase in total surface of the cone ?

With the above information , I am trying to find the answer in the traditional way using formulae, but I am not able to arrive at the answer. Is the data inconsistent in the above question ? If yes, can you explain why ?

share|improve this question
    
Huh. Doesn't look like the percentage is going to be a constant. –  Mike Jul 4 '12 at 10:25

1 Answer 1

The surface area of a (right, circular) cone with radius $r$ and slant height $\ell$ is given $A = \pi r^2 + \pi r \ell~$. Given the height $h$ instead, then we know $r^2 + h^2 = \ell^2~$.

The issue here is that neither expression is linear in the desired variables. So, there's no guarantee that if we have a new cone with radius $r'$, height $h'$ proportional to $r,h$ respectively, that $\ell'$ will be proportional to $\ell$ or that $A'$ will be proportional to $A$. The slant height and area will change proportionally if and only if the radius and height stretch by the same factor (or, to use language consistent with the question, increase by the same percentage).

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.