A right triangle with sides 5cm,12cm and 13cm is rotated about the side 12cm to form a cone. The volume of the cone so formed is:
- A81πcm
3 - B100πcm
3 - C91πcm
3 - D110πcm
3
Solution & Step-by-step Explanation
When a right-angled triangle is rotated about one of its sides forming the perpendicular, that side becomes the height (h) of the cone, and the other perpendicular side becomes the radius (r) of the base. The hypotenuse becomes the slant height (l).
Here, the triangle is rotated about the side 12cm:
Height of the cone (h) = 12cm
Radius of the base (r) = 5cm
Slant height (l) = 13cm
The volume (V) of a cone is given by the formula:
V=
3
1
πr
2
h
Substituting the values:
V=
3
1
×π×5
2
×12
V=
3
1
×π×25×12
V=π×25×4=100πcm
3
Here, the triangle is rotated about the side 12cm:
Height of the cone (h) = 12cm
Radius of the base (r) = 5cm
Slant height (l) = 13cm
The volume (V) of a cone is given by the formula:
V=
3
1
πr
2
h
Substituting the values:
V=
3
1
×π×5
2
×12
V=
3
1
×π×25×12
V=π×25×4=100πcm
3