Find
(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is \( 4.2 \mathrm{~m} \) in diameter and \( 4.5 \mathrm{~m} \) high
(ii) how much steel was actually used, if \( \frac{1}{12} \) of the steel actually used was wasted in making the tank.
Given:
A cylindrical petrol storage tank is $4.2\ m$ in diameter and $4.5\ m$ high.
To do:
We have to find the amount of steel used if $\frac{1}{12}$ of steel actually used was wasted in making the closed tank.
Solution:
Diameter of the cylindrical tank $= 4.2\ m$
This implies,
Radius $(r)=\frac{4.2}{2}$
$=2.1 \mathrm{~m}$
Height $(h)=4.5 \mathrm{~m}$
Therefore,
Lateral surface area $=2 \pi r h$
$=2 \times \frac{22}{7} \times 2.1 \times 4.5$
$=59.4 \mathrm{~m}^{2}$
Total surface area $=2 \pi r(h+r)$
$=2 \times \frac{22}{7} \times 2.1(4.5+2.1)$
$=13.2 \times 6.6$
$=87.12 \mathrm{~m}^{2}$
Let the total area of the sheet be $x \mathrm{~m}^{2}$
Wastage $=\frac{1}{12} x$
Remaining area of sheet $=x-\frac{1}{12} x$
$=\frac{11}{12} x$
This implies,
$\frac{11}{12} x=87.12$
$x=\frac{87.12 \times 12}{11}$
$x=95.04$
Hence, $95.04\ m^2$ of steel was actually used.
Related Articles
- Find the lateral curved surface area of a cylindrical petrol storage tank that is $4.2\ m$ in diameter and $4.5\ m$ high. How much steel was actually used, if $\frac{1}{12}$ of steel actually used was wasted in making the closed tank?
- A rectangular tank \( 15 \mathrm{~m} \) long and \( 11 \mathrm{~m} \) broad is required to receive entire liquid contents from a full cylindrical tank of internal diameter \( 21 \mathrm{~m} \) and length \( 5 \mathrm{~m} \). Find the least height of the tank that will serve the purpose.
- The inner diameter of a circular well is \( 3.5 \mathrm{~m} \). It is \( 10 \mathrm{~m} \) deep. Find(i) its inner curved surface area,(ii) the cost of plastering this curved surface at the rate of Rs. \( 40 \mathrm{per} \mathrm{m}^{2} \).
- In a hospital used water is collected in a cylindrical tank of diameter \( 2 \mathrm{~m} \) and height \( 5 \mathrm{~m} \). After recycling, this water is used to irrigate a park of hospital whose length is \( 25 \mathrm{~m} \) and breadth is \( 20 \mathrm{~m} \). If tank is filled completely then what will be the height of standing water used for irrigating the park?
- A hemispherical tank is made up of an iron sheet \( 1 \mathrm{~cm} \) thick. If the inner radius is \( 1 \mathrm{~m} \), then find the volume of the iron used to make the tank.
- A farmer runs a pipe of internal diameter \( 20 \mathrm{~cm} \) from the canal into a cylindrical tank in his field which is \( 10 \mathrm{~m} \) in diameter and \( 2 \mathrm{~m} \) deep. If water flows through the pipe at the rate of \( 3 \mathrm{~km} / \mathrm{h} \), in how much time will the tank be filled?
- Find the surface area of a sphere of diameter(i) \( 14 \mathrm{~cm} \)(ii) \( 21 \mathrm{~cm} \)(iii) \( 3.5 \mathrm{~m} \).
- The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively \( 2.5 \mathrm{~m} \) and \( 10 \mathrm{~m} \).
- Water is flowing at the rate of \( 2.52 \mathrm{~km} / \mathrm{h} \) through a cylindrical pipe into a cylindrical tank, the radius of the base is \( 40 \mathrm{~cm} \). If the increase in the level of water in the tank, in half an hour is \( 3.15 \mathrm{~m} \), find the internal diameter of the pipe.
- A cylindrical pillar is \( 50 \mathrm{~cm} \) in diameter and \( 3.5 \mathrm{~m} \) in height. Find the cost of painting the curved surface of the pillar at the rate of RS.\( 12.50 \) per \( \mathrm{m}^{2} \).
- Match the following:Column-IColumn-II(P) A cylindrical roller is of length \( 2 \mathrm{~m} \) and diameter \( 84 \mathrm{~cm} \). The number of revolutions ithas to make to cover an area of \( 7920 \mathrm{~m}^{2} \) is(i) 17600(Q) The circumference of the base of a right circular cylinder is \( 176 \mathrm{~cm} \). If the height of the cylinder is \( 1 \mathrm{~m} \), the lateral surface area (in sq. \( \mathrm{cm} \) ) of the cylinder is(ii) 1500(R) The dimensions of a cuboid are (iii) 9 in the ratio \( 5: 2: 1 \). Its volume is 1250 cubic metres. Its total surface area (in sq. \( \mathrm{m} \) ) is(iii) 9(S) If the total surface area of a cubical tank is 486 sq. \( \mathrm{m} \), the length (in \( \mathrm{m} \) ) of one side is(iv) 850
- A cuboidal water tank is \( 6 \mathrm{~m} \) long, \( 5 \mathrm{~m} \) wide and \( 4.5 \mathrm{~m} \) deep. How many litres of water can it hold? \( \left(1 \mathrm{~m}^{3}=1000 t\right) \).
- It is required to make a closed cylindrical tank of height \( 1 \mathrm{~m} \) and base diameter \( 140 \mathrm{~cm} \) from a metal sheet. How many square metres of the sheet are required for the same?
- Find the total surface area of a cone, if its slant height is \( 21 \mathrm{~m} \) and diameter of its base is \( 24 \mathrm{~m} \).
- A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is \( 3 \mathrm{~m} \) and its height is \( 3.5 \mathrm{~m} \)? [Use \( \pi=22 / 7] \).
Kickstart Your Career
Get certified by completing the course
Get Started