question_answer

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

A)  \[59\text{ }\pi \,c{{m}^{2}}\]                          

B)  \[5\pi c{{m}^{2}}\]        

C)  \[100\pi c{{m}^{2}}\]   

D)  \[120\pi c{{m}^{2}}\]

Correct Answer: C

Solution :

(c):

Let ABC be a right triangle with AB=12cm, BC=5 cm and AC= 13cm When this triangle is revolved about AB, it forms a right circular cone of radius =BC=5cm and height AB= 12 cm. \[\therefore {{V}_{1}}\]= Volume of the solid formed= Volume of the cone of radius 5 cm and height 12 cm \[=\frac{1}{3}\times \pi \times 5\times 5\times 12c{{m}^{3}}=100\pi c{{m}^{3}}\]