R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: EXERCISE 15C

A man uses a piece of canvas having an area of $551 {\mathrm{m}}^2$, to make a conical tent of base radius $7 \mathrm{m}$. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately $1 {\mathrm{m}}^2$ find the volume of the tent that can be made with it in ${\mathrm{m}}^3$. [Use $\mathrm{\pi }=\frac{22}{7}$]

A right circular cone is $3.6 \mathrm{cm}$ high and radius of its base is $1.6 \mathrm{cm}$. It is melted and recast into a right circular cone having base radius $1.2 \mathrm{cm}$. Find its height. 

A circus tent is cylindrical to a height of $3$ metres and conical above it. If its diameter is $105 \mathrm{m}$ and the slant height of the conical portion is $53 \mathrm{m}$, calculate the length of the canvas $5 \mathrm{m}$ wide to make the required tent.

An iron pillar consists of a cylindrical portion $2.8 \mathrm{m}$ high and $20 \mathrm{cm}$ in diameter and a cone $42 \mathrm{cm}$ high is surmounting it. Given that $1 {\mathrm{cm}}^3$ of iron weighs $7.5 \mathrm{g}$. If the weight of the pillar is $m \mathrm{kg}$, then find the value of $m.$

From a solid right circular cylinder with height $10 \mathrm{cm}$ and radius of the base $6 \mathrm{cm}$ a right circular cone of the same height and base is removed. Find the volume of the remaining solid in cubic centimeter. (Take $\pi =3.14$.)

(Choose from the following: $753.6, 750.36, 75.36 , 753$)

Water flows at the rate of $10$ metres per minute through a cylindrical pipe $5 \mathrm{mm}$ in diameter. If it takes $k$ minutes to fill a conical vessel whose diameter of the surface is $40 \mathrm{cm}$ and depth $24 \mathrm{cm}$ then find $k$.$$(Express your answer as decimal)

A cloth having an area of $165 {\mathrm{m}}^2$ is shaped into the form of a conical tent of radius $5 \mathrm{m}$. How many students can sit in the tent if a student, on an average, occupies $\frac{5}{7} {\mathrm{m}}^2$ on the ground? [Use $\mathrm{\pi }=\frac{22}{7}$]

A cloth having an area of $165 {\mathrm{m}}^2$ is shaped into the form of a conical tent of radius $5 \mathrm{m}$. If the volume of the cone is $k {\mathrm{m}}^3$, then find the value of $k$ (upto one decimal place). (Take, $\text{π}=\frac{22}{7}$)