Question

Consider a triangle ABC with AB = 2, BC = 5, and AC = 6. If the triangle is rotated around AB, what is the volume of the solid that is generated?

Answer 1

52.33 cubic units.

Explanation:

If we rotate the given triangle around AB, we'll get a circular cone. So, we need to apply the formula to find the volume of a circular cone, which radius would be 5 and height would be 2.

`V=(1)/(3)\pi r^(2)  h`

Replacing all given values, we have:

`V=(1)/(3)(3.14) (5)^(2) (2)=52.33`

Therefore, the volume of the solid generated is 52.33 cubic units.

Answer 2

20/3 cubic unit.

Explanation:

Rotating the triangle with respect to side AB will form a cone with radius as AB and BC as height of the cone. AC will be the slant height.

AB= 2 units = r

and BC= 5 units = h

volume of the cone =
`(1)/(3)\pi r^2h`

putting the values we get

=
`(1)/(3)\pi 2^2*5`

= 20/3 cubic unit.