R. D. Sharma Solutions for Chapter: Mensuration-II (Volumes and Surface Areas of a Cuboid and a Cube), Exercise 4: EXERCISE

A field is $150 \mathrm{m}$ long and $100 \mathrm{m}$ wide. A plot (outside the field) $50 \mathrm{m}$ long and $30 \mathrm{m}$ wide is dug to a depth of $8 \mathrm{m}$ and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?

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

Three cubes whose edges measure $3 \mathrm{c}\mathrm{m}, 4 \mathrm{c}\mathrm{m}$ and $5 \mathrm{c}\mathrm{m}$ respectively are melted to form a new cube. And the surface area of the new cube formed is $k {\mathrm{cm}}^2$, then find the value of $k$.

The cost of preparing the walls of a room $12 \mathrm{m}$ long at the rate of $₹ 1.35$ per square metre is $₹ 340.20$ and the cost of matting the floor at $85$ paise per square metre is $₹ 91.80$. Find the height of the room.

The length of a hall is $18 \mathrm{m}$ and the width $12 \mathrm{m}$. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the wall.

A metal cube of edge $12 \mathrm{c}\mathrm{m}$ is melted and formed into three smaller cubes. The edges of the two smaller cubes are $6 \mathrm{c}\mathrm{m}$ and $8 \mathrm{c}\mathrm{m}$. If the edge of the third smaller cube is $x \mathrm{cm}$, then find the value of $x$.

The dimensions of a cinema hall are $100 \mathrm{m}, 50 \mathrm{m}$ and $18 \mathrm{m}$. How many persons can sit in the hall, if each person requires $150 {\mathrm{m}}^3$ of air?

The external dimensions of a closed wooden box are $48 \mathrm{c}\mathrm{m}, 36 \mathrm{c}\mathrm{m}, 30 \mathrm{c}\mathrm{m}$. The box is made of $1.5 \mathrm{c}\mathrm{m}$ thick wood. How many bricks of size $6 \mathrm{c}\mathrm{m}\times 3 \mathrm{c}\mathrm{m}\times 0.75 \mathrm{c}\mathrm{m}$ can be put in this box?