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If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

7. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained

Q : 8    If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.
 

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When a right-angled triangle is revolved about the perpendicular side, a cone is formed whose,

Height of the cone = Length of the axis= h = 5\ cm

Base radius of the cone = r = 12\ cm

And, Slant height of the cone = l = 13\ cm

We know,

 The volume of a cone = \frac{1}{3}\pi r^2 h

The required volume of the cone formed = \frac{1}{3}\times\frac{22}{7}\times12^2\times5

\\ = \pi\times4\times60 \\ = 240\pi\ cm^3

Now, Ratio of the volumes of the two solids = \\ = \frac{100\pi}{240\pi}

\\ = \frac{5}{12}

Therefore, the required ratio is 5:12

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