The area of the iron sheet required to prepare a cone $24 \text{ cm}$ high with base radius $7 \text{ cm}$ is .......... $\text{cm}^2$ (Take $\pi = \frac{22}{7}$)

$A$ circular wire of radius $42 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio $6:5$. Find the smaller side of the rectangle (in $cm$).

The height of a right circular cylinder is $6 \, m$. $3$ times the sum of the areas of its two circular faces is equal to twice the area of its curved surface. The radius of the base is ...... $m$.

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius $1 \, cm$ and height $5 \, cm$ is ....... $\pi \, cm^3$.

If each edge of a cube is increased by $50 \%$,the percentage increase in surface area is (in $\%$)

The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)