V K Raman and S N Sharma Solutions for Exercise 6: MASTERY TEST-6

 A wire was bent into the form of a circle of radius $7 \mathrm{cm}$. The wire is straightened and bent into the form of a square. Find the area enclosed by the square in ${\mathrm{cm}}^2$.(Write answer without unit).

$\left[\mathrm{Take} \mathrm{\pi }=\frac{22}{7}\right]$

A closed tea chest has its internal dimensions as $60 \mathrm{cm}$ by $40 \mathrm{cm}$ by $30 \mathrm{cm}$. If the area of the tinfoil required to line the box inside is $\mathrm{k} {\mathrm{m}}^2$. Find the value of $k$.

A room is $5 \mathrm{m}$ long, $3 \mathrm{m}$ broad and $2 \mathrm{m}$ high. There is a door $2 \mathrm{m}$ by $1 \mathrm{m}$, and $4$ windows$1 \mathrm{m}$ by $0.5 \mathrm{m}$. Calculate the cost of papering the walls at $₨ 100$ per ${\mathrm{m}}^2$.

Find the volume of metal in an open metal box, cuboid, with external dimensions$50 \mathrm{cm}$ by $40 \mathrm{cm}$ by $32 \mathrm{cm}$, given that it is $2 \mathrm{cm}$ thick throughout in ${\mathrm{cm}}^3$. If volume is $k c{m}^3$, find the value of $k$.

[Hint: Internal dimensions will be $46 \mathrm{cm}$ by $36 \mathrm{cm}$ by$30 \mathrm{cm}$]

The total surface area of a cube is $294 {\mathrm{cm}}^2$. Find its edge and volume.

The dimensions of a cuboid are in the ratio $6 : 5 : 3$ . If the total surface area is $504 {\mathrm{cm}}^2$, find its volume in ${\mathrm{cm}}^3$(Do not write unit).

A full sump contains $60,000$ liters of water. If the length and breadth of the sump are $5 \mathrm{m}$ and  $4 \mathrm{m}$ respectively, find the depth of water in meters.

An International smuggler packed $160$ gold biscuits in a cuboid box of internal dimensions$14 \mathrm{cm}$ by $10 \mathrm{cm}$ by$2 \mathrm{cm}$ . Each gold biscuit was a cuboid in shape with length $7 \mathrm{cm}$ and depth $5 \mathrm{cm}$ . Find the thickness of each gold biscuit.