PRACTICE QUESTIONS COMPETITION WING

Find the slant height of the largest possible cone that can be inserted in a hemisphere of volume $144\mathrm{\pi } {\mathrm{cm}}^3$

In the figure given below, $O$ is the centre of the circle and $\mathrm{OPQR}$ is a rectangle. $A$ is a point on $\mathrm{PO}$ such that $AO=\frac{1}{3}PO$ and $B$ is the midpoint of $OR$. Find the area of the shaded region if $\mathrm{PA}=8 \mathrm{cm}$ and $\mathrm{BR}=4 \mathrm{cm}$(Use $\mathrm{\pi }=3.14)$.

A hollow sphere which has internal and external diameters as $14 \mathrm{cm}$ and $16 \mathrm{cm}$ respectively, is melted and recast into a cone with a height of $16 \mathrm{cm}$. Find the diameter of the base.

A fountain pen with a cylindrical barrel of diameter $2 \mathrm{cm}$ and height $10.5 \mathrm{cm}$, filled with ink, can write $3300$ words. How many words can be written with the pen using $100 \mathrm{ml}$ of ink(Take $1 \mathrm{cc}=1 \mathrm{ml})$

From a solid cube of side $6$ feet, a square hole of side $2$ feet is punched through between a pair of opposite faces. The volume (in cu. feet) of the remaining solid is _____

The radius and slant height of a cone are in the ratio $8:17$. If its curved surface area is $544\mathrm{\pi } {\mathrm{cm}}^2$, then find its volume.

Find the number of coins, $3 \mathrm{cm}$ in diameter and $1 \mathrm{cm}$ in thickness to be melted to form a right-circular cylinder of height $10 \mathrm{cm}$ and diameter $9 \mathrm{cm}$

The sides of a triangle are $45 \mathrm{cm},60 \mathrm{cm}$ and $75 \mathrm{cm}$. Find the length of the altitude drawn to the longest side from its opposite vertex(in $\mathrm{cm}$).