M L Aggarwal Solutions for Exercise 6: Chapter Test

In the adjoining figure, $O$ is the centre of a circular arc and $AOB$ is a line segment. Find the perimeter and the area of the shaded region correct to one decimal place. Take $\pi = 3.14$.

In the figure given below, the radius is $3.5 \mathrm{cm}$. Find the perimeter of the quarter of the circle.

In the figure given below, there are five squares each of side $2 \mathrm{cm}$. Find the radius of the circle and the area of the shaded region. Take $\pi = 3.14$.

Find the radius of a circle if a $90°$ arc has a length of $3.5\mathrm{\pi } \mathrm{cm}$. Hence, find the area of the sector formed by this arc.

Can a pole of $6.5 \mathrm{m}$ long fit into the body of the truck with internal dimensions of $3.5 \mathrm{m}, 3 \mathrm{m} \text{and} 4\mathrm{m}$?

An aquarium took $96$minutes to completely fill with water. Water was filling the aquarium at rate of $25$ litres every $2$minutes. Given that aquarium was $2 \mathrm{m}$ long and $80 \mathrm{cm}$ wide, compute the height of the aquarium.

If the volume of a cube is $V {\mathrm{m}}^3$ its surface area is $S {\mathrm{m}}^2$ and the length of a diagonal is $d$ metres. Prove that $6\sqrt{3}V=Sd$

Three cubes of silver with edges $3 \mathrm{cm}, 4\mathrm{cm} \text{and} 5 \mathrm{cm}$ are melted and recast into a single cube. Find the cost of coating the surface of the new cube with gold at the rate of Rs. $3.50$ per square centimetre.