
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
525.6k+ views
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 , where , 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 , r being the radius. Also, we know that radius is half of diameter thus, radius of coin will be
.
So, on putting the value of in the formula of circumference of circle, we get,
, on solving further, we finally get
.
Now we will use a unitary method to convert 3.14 inch in centimeters.
Since, therefore, we get,
, that is,
.
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.
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
So, on putting the value of
Now we will use a unitary method to convert 3.14 inch in centimeters.
Since,
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.
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