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प्रश्न
A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.
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उत्तर
The double cone so formed is as in figure.
Hypotenuse AC
`=sqrt3^2 +4^2`
`=5 cm.`
Area of
\[= \frac{1}{3} \times \frac{22}{7} \times \frac{12}{5} \times \frac{12}{5} \times 5\]
\[ = \frac{1056}{35}\]
\[ = 30\frac{6}{35}\]
`Delta ABC =1/2 xx AB xx AC`
`1/2 xx AC xx OB`
`=1/2 xx 4 xx 3`
`=1/2 xx 5 xx OB`
`=6`
\[\frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 5 \times OB\]
\[OB = \frac{12}{5}\]
Volume of double cone = volume of cone 1 + cone 2
`=1/3pir^2h_1 + 1/3 pir^2 h_2`
`=1/3pir^2 (h_1 +h_2)`
`=1/3pix^2 (OA + OC)`
\[= \frac{1}{3} \times \frac{22}{7} \times \frac{12}{5} \times \frac{12}{5} \times 5\]
\[ = \frac{1056}{35}\]
\[ = 30\frac{6}{35} {cm}^2\]
