Andhra Pradesh Board Solutions for Chapter: Mensuration, Exercise 7: EXERCISE - 10.3

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 if $1 {\mathrm{cm}}^3$ of iron weighs $7.5 \mathrm{g}$.[Take $\mathrm{\pi }=\frac{22}{7}$]

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 $\left(\text{Take} \mathrm{\pi }=3\frac{1}{7}\right)$. 

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is $7 \mathrm{cm}$.[ Take $\mathrm{\pi }=\frac{22}{7}$]

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

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.[Take $\mathrm{\pi }=\frac{22}{7}$]

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. $\left(\text{Use}: \mathrm{\pi }=\frac{22}{7}\right)$