Chapter 12.3, Problem 8PSB

To determine

To calculate: The number of one liter cans required to paint entire tower.

Answer to Problem 8PSB

The number of one liter cans required are about $24$ .

Explanation of Solution

Given information:

Radius of tower r = 4 m,

Height of tower h = 10 m.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Area of cylinder $=C\times h$

C = Circumference of cylinder and h = height of cylinder

Area of cone $=\frac{1}{2}\times C\times l$

C = Circumference of cone and l = slant height of cone

Calculation:

  

Since the tower is 10 m in total height.

  $AB=10-7=3$

Side AC can be calculated by applying Pythagoras Theorem.

In right angled triangle ABC , we get

  $\begin{array}{l}{\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2\\ {\left(AC\right)}^2={\left(3\right)}^2+{\left(4\right)}^2\\ {\left(AC\right)}^2=9+16\\ {\left(AC\right)}^2=25\\ AC=\sqrt{25}\\ AC=5\end{array}$

Area of cone $=\frac{1}{2}\times C\times l$

  $C=2\pi \times 4=8\pi$

  $l=AC=5$

Area of cone $=\frac{1}{2}\times C\times l$

Area of cone $=\frac{1}{2}\times 8\pi \times 5$

Area of cone $=20\pi$

Area of cylinder $=C\times h$

  $C=2\pi \times 4=8\pi$

  $h=7$

Area of cylinder $=8\pi \times 7$

Area of cylinder $=56\pi$

Area of cylinder $\approx 238.64m^2$

No of cans required = $=\frac{Totalarea}{Heightoftower}=\frac{238.64}{10}=23.86\approx 24$