Telangana Board Solutions for Chapter: Mensuration, Exercise 10: Optional Exercise

A golf ball has diameter equal to $4.1 \mathrm{cm}.$ Its surface has $150$ dimples each of radius $2 \mathrm{mm}$. The total surface area which is exposed to the surroundings$=$_____${\mathrm{cm}}^2$(Assume that the dimples are all hemispherical) $\left[\pi =\frac{22}{7}\right]$.

A cylinder of radius $12 \mathrm{cm}$ contains water to a depth of $20 \mathrm{cm}.$ When a spherical iron ball is dropped in to the cylinder, the level of water is raised by $6.75 \mathrm{cm}.$ Find the radius of the ball. $\left[\pi =\frac{22}{7}\right]$

A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is $4.2 \mathrm{cm}$ and heights of the cylindrical and conical portions are $12 \mathrm{cm}$ and $7 \mathrm{cm}$ respectively. If the volume of the solid toy is $\mathrm{k}\frac{8}{125} {\mathrm{cm}}^3$, then find the value of $k$. $\left[\pi =\frac{22}{7}\right]$

Three metal cubes with edges $15 \mathrm{cm},12 \mathrm{cm}$ and $9 \mathrm{cm}$ respectively are melted together and formed into a single cube. Find the diagonal of this cube.

If the diagonal of the cube is $18\sqrt{k}$ cm, then find the value of k.

A hemispherical bowl of internal diameter $36 \mathrm{cm}$ contains a liquid. This liquid is to be filled in cylindrical bottles of radius $3 \mathrm{cm}$ and height $6 \mathrm{cm}$ How many bottles are required to empty the bowl?