M L Aggarwal Solutions for Chapter: Surface Areas and Volumes, Exercise 3: Exercise 14.3

Find the number of metallic circular disc with $1.5 cm$ base diameter and of height $0.2 cm$ to be melted to form a right circular cylinder of height $10 cm$ and diameter $4.5 cm$.

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 $10 \mathrm{cm}$, find the internal diameter of the sphere

A vessel is in the form of an inverted cone. Its height is $11 \mathrm{cm}$ and the radius of its top, which is open, is $2.5 \mathrm{cm}$. It is filled with water upto the rim. When some lead shots, each of which is a sphere of radius $0.25 \mathrm{cm}$, are dropped into the vessel, $\frac{2}{5}$ of the water flows out. Find the number of lead shots dropped into the vessel.

The surface area of a solid metallic sphere is $1256 c{m}^2$. It is melted and recast into solid right circular cones of radius $2.5 cm$ and height $8 cm$. Calculate the radius of the solid sphere.

The surface area of a solid metallic sphere is $1256 c{m}^2$. It is melted and recast into solid right circular cones of radius $2.5 cm$ and height $8 cm$. Calculate the number of cones recast .$($Use $\mathrm{\pi }=3.14)$

Water in a canal,$5.4 m$ wide and $1.8 m$ deep , is flowing with a speed of $25km/hour.$ How much area can it irrigate in $40$ minutes , if $10 cm$standing water is required for irrigation.

Water is flowing at the rate of $15 \mathrm{km}/\mathrm{h}$through a pipe of diameter $14 \mathrm{cm}$ into a cuboidal pond which is $50 \mathrm{m}$ long and $44 \mathrm{m}$ wide. In what time will the level of water in pond rise by $21 \mathrm{cm}$?

Water is flowing through a cylindrical pipe, of internal diameter of $2 cm$ , into a cylindrical tank of base radius $40 cm$, at the rate of $0.4 m/sec$ . Determine the rise in the level of water in the tank in half an hour.