Question

the largest possible right circular cone is cut out of cube of edge r cm .what is the volume of cone

Answer 1

answer is 1÷12 pi r^3

Answer 2

Answer: $\dfrac{\pi r^3}{12} cm^3$

Step-by-step explanation:

The dimension of the largest possible cone that can be cut out of the cube of edge  r cm  will be

diameter= r cm , radius; R = $\dfrac{r}{2} cm$

height; h = r cm

Now as we know volume of a cone is $\dfrac{1}{3}\pi R^{2} h$

where R is radius and h is height of the cone.

Therefore, $\dfrac{1}{3}\pi\times (\dfrac{r}{2})^2\times r\\\\\Rightarrow\dfrac{1}{3}\pi\times\dfrac{r^3}{4}\\\\\Rightarrow\dfrac{\pi r^3}{12} cm^3$

Hence, the volume is $\dfrac{\pi r^3}{12} cm^3$