PRACTICE QUESTIONS CLASSROOM WING

The diagonal of a square is $\text{'}a\text{'}$ units. Then, the area of the square is _____ square units.

A wire of length $l$ units is bent to form a circle. The radius of the circle so formed is _____ units.

The total surface area of a cone of radius $3$ cm and height $4$ cm is _____ ${\text{cm}}^2\text{.}$

The inner curved surface area of a hollow hemispherical bowl of external radius $14$ cm and thickness $2$ cm is _____ ${\text{cm}}^2\text{.}$

From a square metal sheet of side $5 \mathrm{cm}$, three circular plates of radii $\frac{1}{2} \mathrm{cm}$, $1 \mathrm{cm}$ and $1\frac{1}{2}\mathrm{cm}$ are cut. If the area of the remaining part is equal to the area of a circle, then the area of the circle is _____ ${\mathrm{cm}}^2$

In the figure given below, the area of the shaded region is $44 {\mathrm{cm}}^2$.$O$ is the centre of the semi-circle, $\overline{OE}\perp \overline{OD}$ and $\overline{OC}\perp \overline{AB}$. The area of the region $\mathrm{POQR}$ if $OE=7 \mathrm{cm}$ is _____${\mathrm{cm}}^2$

In the above figure, a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume (in ${\mathrm{cm}}^3$) of the solid(Consider,$\mathrm{\pi }=3.14$ and write the answer upto $2$ decimal places ).

A solid sphere melted and recast into smaller cones.The radii and heights of the cones are equal to the half of the sphere's radius. How many such smaller cones are possible to make?