There is a wooden sphere of radius $6 \sqrt{3} \text{ cm}$. The surface area of the largest possible cube cut out from the sphere will be:

The radius of the base of a solid cone is $9\, cm$ and its height is $21\, cm$. It is cut into $3$ parts by two cuts which are parallel to its base. The cuts are at heights of $7\, cm$ and $14\, cm$ from the base respectively. What is the ratio of the curved surface areas of the top,middle,and bottom parts respectively?

The perimeter of the base of a right circular cone is $132 \, cm$. If the height of the cone is $72 \, cm$,then what is the total surface area (in $cm^2$) of the cone?

$A$ right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is $343 \, c.c.$,then what approximately is the volume of the cone? (in $c.c.$)

The radii of two cylinders are in the ratio $2:3$. The ratio of their heights is $5:3$. The ratio of their volumes is:

The base of a $10\, cm$ high solid cylinder is a semi-circle of radius $7\, cm$. Its total surface area (in $cm^2$) is (Use $\pi = \frac{22}{7}$)