Embibe Experts Solutions for Chapter: Mensuration, Exercise 1: Exercise

A copper bar of volume $110 {\mathrm{cm}}^3$ is drawn into a thin copper wire whose diameter is $5 \mathrm{mm}$. The total length of the copper wire drawn is _____ $\mathrm{m}$. (Correct up to one decimal place and use, $\pi =\frac{22}{7}$)

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?

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 $\mathrm{\pi }=\frac{22}{7}$)

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

The total surface area of the cylinder is $2640 \mathrm{sq} \mathrm{cm}$ and the sum of the external and internal radii is $14 \mathrm{cm}$. If the height of the cylinder is $28 \mathrm{cm}$, what is the difference between the two radii of the cylinder in centimetre? (Take the value of $\mathrm{\pi }=\frac{22}{7}$)

A hollow pipe of length $35 \mathrm{cm}$ is made of $2200 {\mathrm{cm}}^3$ of metal. If the difference between its outer and inner radii is $2 \mathrm{cm}$, then find the measure of the inner radius in $\mathrm{cm}$. (Use $\pi =\frac{22}{7}$)

The barrel of a Montblanc pen is cylindrical in shape and measures $14 \mathrm{cm}$ long and has a diameter of $13.2 \mathrm{mm}$. If ink is filled to the full capacity of the barrel every time, then the number of refills that can be done with a $60 \mathrm{ml}$ bottle of ink, to the nearest whole number, is undefined. [Assume $\mathrm{\pi }=\frac{22}{7} \&\hspace{0.17em}1 \mathrm{ml}=1 {\mathrm{cm}}^3$]

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 $\mathrm{\pi }=\frac{22}{7}$)