Question

A right triangle ABC with sides 6m, 8m and 10m is revolved about the side 8m, then the volume of the solid so obtained is a 25π b 50π c 96π d 150π​

Answer 1

Answer:

The volume of the obtained solid by revolving the triangle is 96π cm³.

Step-by-step explanation:

The given sides of the right-angle triangle are 6 m,8 m, and 10 m.

Then 10 m will be the hypotenuse of the right-angle triangle. Because according to the Pythagorean theorem,

Hypotenuse² = adjascent² + opposite²

            10² = 8² + 6²

           100 = 84 + 36

The triangle is revolved along with the side 8 m. Then the obtained solid will be a cone with a radius of 6 m and a height of 8 m.

The formula to find the volume of the cone is given as follows,

      $V =\dfrac{\pi r^2h}{3}$

Where 'r' and 'h' are the radius and height of the cone respectively.

By substituting the values ⇒

     $V =\dfrac{\pi\times 6^2\times 8}{3}=\dfrac{\pi\times 36\times 8}{3}\\\\V=96\pi\ cm^3$

Hence the volume of the obtained cone is 96π cm³.