Given: The surface area of a sphere is $154\ cm^{2}$.To do: We have to find the volume of the sphere.Solution:Let $r$ be the radius of the sphere.Therefore, Surface area of the sphere$=4\pi r^2$$=154$This implies, $r^2=\frac{154}{4\pi}$$r^2=\frac{154}{4\times\frac{22}{7}}$$r^2=\frac{154\times7}{4\times22}$$r^2=\frac{49}{4}$$r^2=\frac{7^2}{2^2}$$r=\frac{7}{2}$Volume of the sphere $=\frac{4}{3} \pi (\frac{7}{2})^{3}$$=\frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}$$=\frac{11 \times 7 \times 7}{3}$$=179.67 ... Read More

Given:A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of \( Rs. 4989.60 \). The cost of white-washing is \( Rs. 20 \) per square metre.To do:We have to find the(i) inside surface area of the dome, (ii) volume ... Read More

Given:Twenty seven solid iron spheres, each of radius \( r \) and surface area \( \mathrm{S} \) are melted to form a sphere with surface area \( S^{\prime} \).To do:We have to find the(i) radius \( r^{\prime} \) of the new sphere, (ii) ratio of \( \mathrm{S} \) and \( ... Read More

 Given:A capsule of medicine is in the shape of a sphere of diameter $3.5\ mm$.To do:We have to find the volume of medicine (in $mm^3$) needed to fill the capsule.Solution:Diameter of the spherical medicine capsule $= 3.5\ mm$This implies, Radius of the spherical medicine capsule $= \frac{3.5}{2}\ mm$$=\frac{35}{20}\ mm$$=1.75\ mm$Volume ... Read More

 Given:A matchbox measures \( 4 \mathrm{~cm} \times 2.5 \mathrm{~cm} \times 1.5 \mathrm{~cm} \). To do:We have to find the volume of a packet containing 12 such boxes.Solution:Length of the matchbox $l=4\ cm$Breadth of the matchbox $b=2.5\ cm$Height of the matchbox $h=1.5\ cm$This implies, The matchbox is in the shape of a ... Read More

Given:A cuboidal water tank is $6\ m$ long, $5\ m$ wide and $4.5\ m$ deep.To do:We have to find the number of litres of water it can hold.Solution:Length of the water tank $(l) = 6\ m$Breadth of the tank $(b) = 5\ m$Depth of the tank $(h) = 4.5\ m$Therefore, ... Read More

Given:A cubical vessel is $10\ m$ long and $8\ m$ wide. To do:We have to find the height of the vessel to hold $380$ cubic metres of a liquid.Solution:Length of the vessel $(l) = 10\ m$Breadth of the vessel $(b) = 8\ m$Let the height of the vessel be $h$.Therefore, Volume ... Read More

Given:A cuboidal pit $8\ m$ long, $6\ m$ broad and $3\ m$ deep.To do:We have to find the cost of digging a cuboidal pit $8\ m$ long, $6\ m$ broad and $3\ m$ deep at the rate of $Rs.\ 30$ per $m^3$.Solution:Length of the pit $(l) = 8\ m$Width of ... Read More

 Given:The capacity of a cuboidal tank is 50000 litres of water.Length and depth of the tank are respectively \( 2.5 \mathrm{~m} \) and \( 10 \mathrm{~m} \).To do:We have to find the breadth of the tank.Solution:Length of the tank $l=2.5\ m$Let the breadth of the tank be $b$Depth(Height) of the ... Read More

Given:A village having a population of $4000$ requires $150$ litres of water per head per day. It has a tank measuring $20\ m \times 15\ m \times 6\ m$.To do:We have to find the number of days the water of the tank will last.Solution:Population of the village $= 4000$Water required ... Read More