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TN XII Math
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Integral Calculus and its applications
0
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Derive the formula for the volume of a right circular cone with radius $'r'$ and height $'h'$.
tnstate
class12
bookproblem
ch7
sec-1
exercise7-4
p118
q15
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asked
Apr 30, 2013
by
poojasapani_1
edited
Apr 30, 2013
by
poojasapani_1
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1 Answer
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Toolbox:
Area bounded by the curve $t=f(x),$ the x-axis and the ordinates $x=a,x=b$ is $\int \limits_a^b f(x) dx $ or $ \int \limits _a^b y dx $
If the curve lies below the x-axis for $a \leq x \leq b,$ then the area is $\int \limits_a^b (-y) dx=\int \limits_a^b (-f(x))dx$
http://clay6.com/mpaimg/tn7.415.JPG
Step 1:
A right circular cone of radius r,height h, generated when the area bounded by the line OA(Where a is the point(h,r))
Step 2:
The x-axis and $x=h$ is rotated about the x-axis
Equation of OA is $\large\frac{y}{x}=\frac{r}{h}$$=>y=\large\frac{r}{h}$$x$
The volume of the cone$=\pi\int\limits_0^h y^2dx=\pi\int\limits_0^h \large\frac{r^2}{h^2}$$x^2dx$
answered
Aug 16, 2013
by
meena.p
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