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$$=8π.$$

So, perimeter of the base of cone is$$2πr$$.

So,$$2πr=8π.$$

or,$$r=4.$$

radius of the circle is 12 cm.

So,slant height of the cone is 12 cm.

So, height of the cone$$=√(12^2-4^2)$$

$$=√128=8√2.$$

So,V$$=(1/3)π4^2×8√2.$$

and S$$=π×4×√(h^2+r^2)=4π×12.$$

So,V:S$$=8√2:9.$$

C is correct choice.

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