# Science:Math Exam Resources/Courses/MATH103/April 2009/Question 05 (a)

MATH103 April 2009
Other MATH103 Exams

### Question 05 (a)

A carrot has the shape formed by revolving the region under the graph of

${\displaystyle f(x)={\sqrt {14-x}}}$

for ${\displaystyle 0\leq x\leq 12}$ cm about the x axis. The concentration of vitamin A is found to vary in the carrot with x according to

${\displaystyle c(x)={\frac {1}{12}}e^{-x/12}{\frac {\text{mg}}{{\text{cm}}^{3}}}}$

What is the volume of the carrot?

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