Answer:
C)49π
Step-by-step explanation:
Given:
As in given figure there are two right triangle,
Let the bigger right triangle be ABC
and the smaller right angle be ADE
Finding length of hypotenuse of ΔABC
h [tex]=\sqrt{12^{2} +5^{2} }\\ =13[/tex]
h=AC=13
Now as the two right triangles are similar as both have one angle common i.e. A, and one right angle i.e. 90 degree.
As ΔABC is similar to ΔADE
BC/AC=DE/AE
5/13=r/(12-r)
r= (12-r)0.384
r= 4.615-0.384r
r+0.384r =4.615
1.384r=4.615
r=4.615/1.384
r=3.33
Now volume of the inscribed sphere
volume=4/3πr^3
putting value of r=3.33 in above
volume=4/3π(3.33^3)
=49.23π
= 49π !
