R. D. Sharma Solutions for Chapter: Surface Area and Volume of a Cuboid and Cube, Exercise 2: EXERCISE

A cubical vessel is $10 \mathrm{m}$ long and $8 \mathrm{m}$ wide. How high must it be made to hold $380$ cubic meters of a liquid?

Two cubes, each of volume $512 {\mathrm{cm}}^3$ are joined end to end. If the surface area of the resulting cuboid is $k {\mathrm{cm}}^2$, find $k$.

A box with lid is made of $2 \mathrm{cm}$ thick wood. Its external length, breadth and height are $25 \mathrm{cm}, 18 \mathrm{cm}$ and $15 \mathrm{cm}$ respectively. How much cubic $\mathrm{cm}$ of a liquid can be placed in it? Also, find the volume of the wood used in it.

A river $3 \mathrm{m}$ deep and $40 \mathrm{m}$ wide is flowing at the rate of $2 \mathrm{km}$ per hour. How much water will fall into the sea in a minute?

How many cubic centimetres of iron are there in an open box whose external dimensions are $36 \mathrm{cm}, 25 \mathrm{cm}$ and $16.5 \mathrm{cm}$, the iron being $1.5 \mathrm{cm}$ thick throughout? If $1 \mathrm{cubic} \mathrm{cm}$ of iron weighs $15 \mathrm{g}$, find the weight of the empty box in $\mathrm{kg}$.

A rectangular container, whose base is a square of side $5 \mathrm{cm}$, stands on a horizontal table, and holds water up to $1 \mathrm{cm}$ from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and $2 \mathrm{cubic} \mathrm{cm}$ of water overflows. Calculate the volume of the cube and also the length of its edge.

A rectangular tank is $80 \mathrm{m}$ long and $25 \mathrm{m}$ broad. Water flows into it through a pipe whose cross-section is $25 {\mathrm{cm}}^2$, at the rate of $16 \mathrm{km}$ per hour. If the level of the water rises by $k \mathrm{cm}$ in the tank in $45$ minutes, then find the value of $k$.

Water in a rectangular reservoir having base $80 \mathrm{m}$ by $60 \mathrm{m}$ is $6.5 \mathrm{m}$ deep. In what time can the water be emptied by a pipe of which the-cross-section is a square of side $20 \mathrm{cm}$, if the water runs through the pipe at the rate of $15 \mathrm{km}/\mathrm{hr}$?