A cube is placed inside a cone of radius $20$ cm and height $10$ cm , one of its faces being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm ) of side of the cube?

A spherical ball of lead,$3$ cm in diameter, is melted and recast into three spherical balls. The diameter of two of these balls are $1.5$cm and $2$ cm respectively. The diameter of the third ball is-

The curved surface area of a right circular cylinder of height $14 cm$ is $88 c{m}^2$. Find the diameter of the base of the cylinder.

$\mathrm{D}$ and $\mathrm{E}$ are points on side $\mathrm{AB}$ and $\mathrm{AC}$ of $\mathrm{\Delta } \mathrm{ABC}$. $\mathrm{DE}$ is parallel to $\mathrm{BC}$. If $\mathrm{AD} : \mathrm{DB} =2: 5$ and area of $\mathrm{\Delta } \mathrm{ABC}$ is $98$ $cm sq$, what is the area (in $cm sq$) of quadrilateral $\mathrm{BDEC}$?

The two circle of radii $6 \mathrm{cm}$ and $3 \mathrm{cm}$ centered at the point P and Q respectively. A transverse common tangent AC to both circles cuts line joining P and Q at the point B such that $\mathrm{AB}=8 \mathrm{cm}$. Calculate the length (in cm) of PQ.

For the circle shown below, find the length (in cm) of the largest chord of the circle.