Question 76

A solid sphere of radius $$r$$ is melted and with that material a solid cone and twenty two identical solid cubes were made. If the height of cone and edge of each cube are each equal 9 to half the radius of the sphere, then the ratio of the radius of the cone to its height is

Solution

Volume of the sphere is

$$=(4/3)πr^3.$$

height of cone r/2.

let say radius of cone is a.

So, volume of cone is

$$=(1/6)πa^2r.$$

side of cube is $$=r/2.$$

volume of cube$$=r^3/8.$$

So,$$(4/3)πr^3=(1/3)πa^2r+r^3/8.$$

So,$$a=(√11/2)r$$.

So, height: radius$$=√11:1$$.

B is correct choice.

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