Neha Tyagi and Amit Rastogi Solutions for Chapter: Surface Areas and Volumes, Exercise 4: Exercise

The barrel of a fountain pen, cylindrical in shape, is $7 \mathrm{cm}$ long and $5 \mathrm{mm}$ in diameter. A full barrel of ink in the pin is used up on writing $3300$ words on an average. How many words can be written in a bottle of ink containing one-fifth of a litre?

Water flows at the rate of $10 \mathrm{m} {\min }^{-1}$ through a cylindrical pipe $5 \mathrm{mm}$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 \mathrm{cm}$ and depth $24 \mathrm{cm}$?

A  factory manufactures $120000$ pencils daily. The pencils are cylindrical in shape each of length $25 c\mathrm{m}$ and circumference of base as $1.5 \mathrm{cm}$. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $₹0.05 \mathrm{per} {\mathrm{dm}}^2$.

Water is flowing at the rate of $15 {\mathrm{kmh}}^{-1}$ through a pipe of diameter $14 \mathrm{cm}$ into a cuboidal pond which is $50 \mathrm{cm}$ long and $44 \mathrm{cm}$ wide. In what time will the level of water in pond rise by $21 \mathrm{cm}$?

A solid iron cuboidal block of dimensions $4.4 \mathrm{m} \times 2.6 \mathrm{m} \times 1\mathrm{m}$ is recast into a hollow cylindrical pipe of internal radius $30 \mathrm{cm}$ and thickness $5 \mathrm{cm}.$ Find the length of the pipe.

$500$ persons are taking a dip into a cuboidal pond which is $80$ long and $50$ broad. What is the rise of water level in the pond, if the average displacement of the water by a person is  $0.04 {\mathrm{m}}^3$?

 A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21} {\mathrm{m}}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building in $\mathrm{m}$? 

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimensions of cuboid are $10\mathrm{cm}, 5\mathrm{cm} \mathrm{and} 4\mathrm{cm}$. The radius of each of the conical depressions is $3\mathrm{cm}$. Find the volume of the wood in the entire stand.