Mahabir Singh Solutions for Chapter: Surface Areas and Volumes, Exercise 1: MATHEMATICAL REASONING

A metal sheet $27\mathrm{cm}$ long. $8\mathrm{cm}$ broad and $1\mathrm{cm}$ thick is melted into a cube. Find the difference between surface areas of two solids.

The height of a cone is equal to its base diameter. Then slant height of the cone is

The length of the longest rod that can be kept in a cuboidal room of dimensions $10 \mathrm{m}\times 10 \mathrm{m}\times 5 \mathrm{m}$ is __________.

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is $50\%$ more than its height. If the diameter is same for both the bowl and the cylinder, then the amount of the beverage that can be poured from the bowl into the cylindrical vessel is

The volume of a cylinder of radius $\mathrm{r}$ is $\frac{1}{4}$ of the volume of rectangular box with a square base of side length $\mathrm{x}$. If the cylinder and the box have equal heights, what is the value of $\mathrm{r}$ in terms of $\mathrm{x}?$

The edge of a cube is $20\mathrm{cm}$. How many small cubes of edge $5\mathrm{cm}$ can be formed from this cube?

The volume of two spheres are in the ratio $64:27$. the difference of their surface areas, if the sum of their radii is $7$ units, is ______

The radii of two cylinders are in the ratio $2:3$ and their heights are in the ratio of $5:3$ The ratio of their volumes is ___________