Telangana Board Solutions for Chapter: Mensuration, Exercise 9: Exercise

A metallic sphere of radius $4.2 \mathrm{cm}$ is melted and recast into the shape of a cylinder of radius $6 \mathrm{cm}$. Find the height of the cylinder in $\mathrm{cm}$ (correct to two decimal places).

Three metallic spheres of radii $6 \mathrm{cm}, 8 \mathrm{cm}$ and $10 \mathrm{cm}$ respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere in $\mathrm{cm}$.

A $20 \mathrm{m}$ deep well of diameter $7 \mathrm{m}$ is dag and the earth got by digging is evenly spread out to form a rectangular platform of base $22 \mathrm{m}\times 14 \mathrm{m}$. Find the height of the platform in $\mathrm{m}$.

A well of diameter $14 \mathrm{m}$ is dug $15 \mathrm{m}$ deep. The earth taken out of it has been spread evenly to form circular embankment all around the wall of width $7 \mathrm{m}$. Find the height of the embankment.

A container shaped a right circular cylinder having diameter $12 \mathrm{cm}$ and height $15 \mathrm{cm}$ is full of ice cream. The ice cream is to be filled into cones of height $12 \mathrm{cm}$ and diameter $6 \mathrm{cm}$, making a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream

How many silver coins, $1.75 \mathrm{cm}$ in diameter and thickness $2 \mathrm{mm}$, need to be melted to form a cuboid of dimensions $5.5 \mathrm{cm}\times 10 \mathrm{cm}\times 3.5 \mathrm{cm}$?

A vessel is in the form of an inverted cone. Its height is $8 \mathrm{cm}$ and the radius of its top is $5 \mathrm{cm}$ It is filled with water up to the rim. When lead shots, each of which is a sphere of radius $0.5 \mathrm{cm}$ are dropped into the vessel, $\frac{1}{4}$ of the water flows out. Find the number of lead shots dropped into the vessel.

A solid metallic sphere of diameter $28 \mathrm{cm}$ is melted and recast into a number of smaller cones, each of diameter $4\frac{2}{3} \mathrm{cm}$ and height $3 \mathrm{cm}$. Find the number of cones so formed.