Question

An artist wants to draw the following design. If his quill can hold enough paint to draw a line 400 mm long in one go, how many times would he need to refill his quill? (The design is shown in black.)

• A. 1 time
• B. 2 times
• C. 3 times
• D. 4 times

Answer 1

The correct option is D 4 times

The given design can be broken down as:

Calculating the circumference of each part, we find:

$PartA:\left(Semicircle\right)$

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{400mm}{2}=200mm$

$\text{Perimeter}=\pi \times Radius=200\pi mm$

$PartB:\left(Semicircle\right)$

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{200mm}{2}=100mm$

$\text{Perimeter}=\pi \times Radius=100\pi mm$

$PartC:\left(Semicircle\right)$

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{100mm}{2}=50mm$

$\text{Perimeter}=\pi \times Radius=50\pi mm$

$PartD:\left(Circle\right)$

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{50mm}{2}=25mm$

$\text{Perimeter}=2\times \pi \times Radius=2\times \pi \times 25=50\pi mm$

$\text{Total perimeter of the design:}$
$200\pi +100\pi +50\pi +50\pi =400\pi mm$

$\text{Hence, if the quill can draw a line of length}\text{400 mm in one go, the artist would need}\text{to refill it}\pi \text{times to complete the design.}$

$\text{Now,}\pi >3$

$\therefore \text{The artist would need to refill his quill}$ $\text{4 times to complete the design.}$