O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Find the length of the diagonal and the volume of the cube whose each edge is $2 \mathrm{m}$.

Find the length of the diagonal and the volume of the cube whose each edge is $5 \mathrm{m}$.

Find the length of the diagonal and the volume of the cube whose each edge is $8 \mathrm{cm}$.

 Find the volume and total surface area of a cube, if its edge is $12 \mathrm{cm}$.

The length, breadth and height of a rectangular solid are in the ratio of $5:4:2$. If the total surface area is $1216 {\mathrm{cm}}^2$, then find the length, breadth and height of the solid.

How many rectangular blocks, each $2\frac{1}{2} \mathrm{cm}$ by $2 \mathrm{cm}$ by $1\frac{1}{2} \mathrm{cm}$ can be packed in a box $90 \mathrm{cm}$ by $78 \mathrm{cm}$ by $42 \mathrm{cm}$, internal measurements? Also, find the number of $4 \mathrm{cm}$ cubes that can be packed in this box with faces parallel to the sides.

A certain quality of wood costs $₹250$ per ${\mathrm{m}}^3$. A solid cubical block of such wood is bought for $₹182.25$. Calculate the volume of the block and the edge length of the block.

$50$ students sit in a classroom. Each student requires $9 {\mathrm{m}}^2$ on floor and $108 {\mathrm{m}}^3$ in space. If the length of the room is $25 \mathrm{m}$, find the breadth and height.