Question 75
From a circle of radius 12cm centered at O, a sector OAB of are length $$8\pi$$ cm is cut and from it a cone is formed by joining OA and OB. If the volume of the cone is V cubic cm and its lateral surface area is S square cm, then V:S =
Solution
Length of the arc is$$=8Ο.$$
So, perimeter of the base of cone is$$2Οr$$.
So,$$2Οr=8Ο.$$
or,$$r=4.$$
radius of the circle is 12 cm.
So,slant height of the cone is 12 cm.
So, height of the cone$$=β(12^2-4^2)$$
$$=β128=8β2.$$
So,V$$=(1/3)Ο4^2Γ8β2.$$
and S$$=ΟΓ4Γβ(h^2+r^2)=4ΟΓ12.$$
So,V:S$$=8β2:9.$$
C is correct choice.
Get AI Help
Create a FREE account and get:
- Download Maths Shortcuts PDF
- Get 300+ previous papers with solutions PDF
- 500+ Online Tests for Free
