Question

The diameter of a half penny is an inch, what is the length of a piece of string which would just surround its curved edge?

Answer 1

Hint: Half penny is a currency which is a coin and we know that coin is in a circular shape. So, basically in this question we will find the circumference of a circle having diameter 1 inch. Also, 1 inch is equal to 2.54cm and circumference of the circle is given by $2\pi r$, where $2r=d$, d being the diameter.

Complete step-by-step answer:
It is given in the question that the diameter of a half-penny is 1 inch. It is also given that the edges of a half-penny are wounded by the string and we have to find the length of string required to completely wound the half-penny.
Now, the length of string is exactly equal to the circumference of the semi-circle. So, we will find the circumference of the circle to find the length of string required.
Now, we know that circumference of the circle is given by $2\pi r$, r being the radius. Also, we know that radius is half of diameter thus, radius of coin will be
$=\dfrac{diameter}{2}$
$=\dfrac{1}{2}=0.5\text{ }inch$.
So, on putting the value of $radius,r=0.5\text{ }inch$ in the formula of circumference of circle,$2\pi r$ we get,
\[Circumference\text{ }=2\pi r=2\times 3.14\times 0.5\], on solving further, we finally get
\[Circumference\text{ }=3.14\text{ }inch\].
Now we will use a unitary method to convert 3.14 inch in centimeters.
Since, $1inch=2.54cm$ therefore, we get,
$3.14inch=3.14\times 2.54cm$, that is,
$=7.97cm$.
Thus, the circumference of the circle will be 7.97cm, also the length of string required is also 7.97cm.

Note: Many times students may confuse the word half-penny and they may assume that the coin is half, that is in the shape of a semi-circle, which is wrong. Actually half a penny is a currency and it is a complete circular shape, thus we will find the circumference of a circle and not a semi-circle.