Tamil Nadu Board Solutions for Chapter: Mensuration, Exercise 17: Exercise 7.4

An aluminium sphere of radius $12 \mathrm{cm}$ is melted to make a cylinder of radius $8 \mathrm{cm}.$ The height of the cylinder is $k \mathrm{cm}$. Find the value of $k$.

Water is flowing at the rate of $15 \mathrm{km}$ per hour through a pipe of diameter $14 \mathrm{cm}$ into a rectangular tank which is $50 \mathrm{m}$ long and $44 \mathrm{m}$ wide. The time in which the level of water in the tanks will rise by $21 \mathrm{cm}$ is $k$ hours. Find the value of $k$.

A conical flask is full of water. The flask has base radius $r$ units and height$h$ units, the water poured into a cylindrical flask of base radius $xr$ units. The height of water in the cylindrical flask is $\frac{h}{k{x}^2}$ units. Find the value of $k$.

A solid right circular cone of diameter $14 \mathrm{cm}$ and height $8 \mathrm{cm}$ is melted to form a hollow sphere. If the external diameter of the sphere is $10 \mathrm{cm}$, then the internal diameter is $k \mathrm{cm}$. Find the value of $k$.

Seenu's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions $2 \mathrm{m}\times 1.5 \mathrm{m}\times 1 \mathrm{m}$. The overhead tank has its radius of $60 \mathrm{cm}$ and height$105 \mathrm{cm}$. The volume of the water left in the sump after the overhead tank has been completely filled with water from the sump which has been full, initially is $k {\mathrm{cm}}^3$. Find the value of $k$.

The internal and external diameter of a hollow hemispherical shell are $6 \mathrm{cm}$ and $10 \mathrm{cm}$ respectively. If it is melted and recast into a solid cylinder of diameter $14 \mathrm{cm},$ the height of the cylinder is $k \mathrm{cm}$. Find the value of $k$.

A solid sphere of radius $6 \mathrm{cm}$ is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is $5 \mathrm{cm}$ and its height is $32 \mathrm{cm},$ then find the thickness of the cylinder.

A hemispherical bowl is filled up to the brim with juice. The juice is poured into a cylindrical vessel whose radius is $50\%$ more than its height. If the diameter is same for both the bowl and the cylinder then the percentage of juice that can be transferred from the bowl into the cylindrical vessel is $k\%$. Find the value of $k$.