NCERT Solutions for Chapter: Mensuration, Exercise 1: Exercise

The terrace of a house measures $40’\times 30’$(Consider $1’=0.30 \mathrm{m}$). The rainwater collected on the terrace is sent through a pipe and it completely fills a cylindrical tank of diameter $1.4 \mathrm{m}$ and height $0.5 \mathrm{m}$. Find the height to which the rainwater is collected on the terrace in metre. (Calculate up to $3$ decimal places, Use $\mathrm{\pi }=\frac{22}{7}$)

A rectangular box with lid is made up of certain metal sheet of thickness $1 \mathrm{cm}$. Its outer dimensions are $50 \mathrm{cm}, 40 \mathrm{cm}$, and $20 \mathrm{cm}$. If the weight of the metal is $4 \mathrm{g}$ per ${\mathrm{cm}}^3$, then the weight of the box is _____.

The ratio of the volumes of two cubes is $729:1331$. What is the ratio of their total surface areas?

In a chemical lab, Sowmya transfers all liquid from a beaker filled to the brim to a graduated cylinder. Find the height of the liquid in the graduated cylinder in $\mathrm{cm}$. (Consider $1"= 2.5 \mathrm{cm}$)

(Use $\pi =\frac{22}{7}$)

A metal cylindrical disc of base radius $4 \mathrm{cm}$ and height $1.5 \mathrm{cm}$ is melted and recast into a cylindrical bar of base radius $2 \mathrm{cm}$. Find the ratio of the total surface area of the disc to that of the bar.

Metal cubes having $5 \mathrm{mm}$ edge are to be melted to form a right circular cylinder of height $10 \mathrm{cm}$ and diameter $3.5 \mathrm{cm}$. How many metal cubes of this size are required to make the cylinder?

A metal cube of  $6 \mathrm{cm}$ edge is immersed in a glass cylinder with diameter $14 \mathrm{cm}$. The initial height of water in the cylinder is $12 \mathrm{cm}$. The total height to which water rises in the cylinder after the cube is immersed is $13.4 \mathrm{cm}$.

(Answer in up to one decimal place, Use $\mathrm{\pi }=\frac{22}{7}$)

Given is a square. The numbers 16, 20 and 32 denote the areas of respective regions.