Given:Chords of congruent circles subtend equal angles at their centres.To do:We have to prove that the chords are equal.Solution:  Let $c_{1}$ and $C_{2}$ be two congruent circles, $AB$ and $PQ$ are their chords respectively. Let us join $OA$ and $OB$ in circle $C_{1}$.Similarly, in cirlcle $C_{2}$, join $MP$ and $MQ$.In $\vartriangle OAB$ ... Read More

Given:Diameter of the roller$=84\ cm$Length of the roller$=120\ cm$.The number of revolutions taken to level the playground$=500$.To do: We have to find the area of the playground in $m^2$.Solution:Radius of the roller$=\frac{84}{2}\ cm=42\ cm$.We know that, The curved surface area of a cylinder of radius $r$ and height $h$ is $2 ... Read More

Given:A cylindrical pillar is $50\ cm$ in diameter and $3.5\ m$ in height. To do:We have to find the cost of painting the curved surface of the pillar at the rate of $12.50$ per $m^2$.Solution:Diameter of the cylindrical pillar $= 50\ cm$This implies, Radius of the pillar $(r)=\frac{50}{2}\ cm$$=25\ cm$$=\frac{1}{4} \mathrm{~m}$Height ... Read More

Given:The curved surface area of a right circular cylinder is $4.4\ m^2$.The radius of the base of the cylinder is $0.7\ m$.To do:We have to find its height. Solution:The curved surface area of the cylinder $= 4.4\ m^2$Radius of the base $(r) = 0.7\ m$Therefore, Height of the cylinder $=\frac{\text { ... Read More

Given:The inner diameter of a circular well is $3.5\ m$. It is $10\ m$ deep. To do:We have to find:(i) Its inner curved surface area.(ii) the cost of plastering this curved surface at the rate of $Rs.\ 40$ per $m^2$.Solution:The inner diameter of the well $= 3.5\ m$This implies, Radius $(r)=\frac{3.5}{2}$$=1.75 ... Read More

Given:In a hot water heating system, there is a cylindrical pipe of length $28\ m$ and diameter $5\ cm$. To do:We have to find the total radiating surface in the system.Solution:Diameter of the pipe $= 5\ cm$This implies, Radius of the pipe $(r)=\frac{5}{2} \mathrm{~cm}$Length of the pipe $(h)=28 \mathrm{~m}$$=2800 \mathrm{~cm}$Therefore, The ... Read More

 Given:A cylindrical petrol storage tank is $4.2\ m$ in diameter and $4.5\ m$ high. To do:We have to find the amount of steel used if $\frac{1}{12}$ of steel actually used was wasted in making the closed tank.Solution:Diameter of the cylindrical tank $= 4.2\ m$This implies, Radius $(r)=\frac{4.2}{2}$$=2.1 \mathrm{~m}$Height $(h)=4.5 \mathrm{~m}$Therefore, Lateral ... Read More

Given:The frame has a base diameter of \( 20 \mathrm{~cm} \) and height of \( 30 \mathrm{~cm} \). A margin of \( 2.5 \mathrm{~cm} \) is to be given for folding it over the top and bottom of the frame.To do:We have to find how much cloth is required for ... Read More

Given:Each pen holder was to be of radius $3\ cm$ and height $10.5\ cm$.There were $35$ competitors.To do:We have to find the cardboard that was required to be bought for the competition.Solution:Radius of the cylindrical pen holder $(r) = 3\ cm$Height of the pen holder $(h) = 10.5\ cm$Therefore, The ... Read More

Given: \( \mathrm{ABC} \) and \( \mathrm{BDE} \) are two equilateral triangles such that \( \mathrm{D} \) is the mid-point of \( \mathrm{BC} \).\( \mathrm{AE} \) intersects \( \mathrm{BC} \)To do:We have to show that(i) \( \operatorname{ar}(\mathrm{BDE})=\frac{1}{4} \operatorname{ar}(\mathrm{ABC}) \)(ii) \( \operatorname{ar}(\mathrm{BDE})=\frac{1}{2} \operatorname{ar}(\mathrm{BAE}) \)(iii) \( \operatorname{ar}(\mathrm{ABC})=2 \) ar \( (\mathrm{BEC}) \)(iv) \( ... Read More