Telangana Board Solutions for Chapter: Mensuration, Exercise 6: Exercise

An iron pillar consists of a cylindrical portion of $2.8$ $\mathrm{m}$ height and $20$ $\mathrm{cm}$ in diameter and a cone of $42$ $\mathrm{cm}$ height surmounting it. Find the weight of the pillar in $\mathrm{kg}$, if $1$ ${\mathrm{cm}}^3$ of iron weighs $7.5$ $\mathrm{g}$.

A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is $7$ $\mathrm{cm}$ and its volume is $\frac{3}{2}$ of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to $2$ places of decimal. (Take$\pi =3\frac{1}{7}$).

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is $7 \mathrm{cm}$ in ${\mathrm{cm}}^3$.

A cylindrical mug of radius $5$ $\mathrm{cm}$ and height $9.8$ $\mathrm{cm}$ is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the mug. The radius of the hemisphere is $3.5$ $\mathrm{cm}$ and height of conical part $5$ $\mathrm{cm}$. Find the volume of water left in the tub. (Take$\pi =\frac{22}{7}$)

In the adjacent figure, the height of a solid cylinder is $10 \mathrm{cm}$ and diameter is $7 \mathrm{cm}$. Two equal conical holes of radius $3 \mathrm{cm}$ and height $4 \mathrm{cm}$ are cut off as shown the figure. Find the volume of the remaining solid.

Spherical marbles of diameter $1.4$ $\mathrm{cm}$ are dropped into a cylindrical beaker of diameter $7$ $\mathrm{cm}$, which contains some water. Find the number of marbles that should be dropped in to the beaker, so that water level rises by $5.6$ $\mathrm{cm}$.

A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are $15$ $\mathrm{cm}$ by $10$ $\mathrm{cm}$ by $3.5$ $\mathrm{cm}$. The radius of each of the depression is $0.5$ $\mathrm{cm}$ and the depth is $1.4$ $\mathrm{cm}$. Find the volume of wood in the entire stand in the cubic centimetres.