Question

Diameter of a circle is $7.12\text{ cm}$ then the radius is
A. $35.6\text{ cm}$
B. $3.56\text{ cm}$
C. $356\text{ cm}$
D. $0.356\text{ cm}$

Answer 1

Hint: We know that the condition between radius and diameter will be double of radius. We use the condition and divide the length of the given diameter with 2 to get the length of the radius.

Complete step by step solution:
It is given that the diameter of a circle is $7.12\text{ cm}$. We have to find the radius of the circle.
Let us assume the radius of the circle is $r\text{ cm}$.
We know that for a circle with radius $r\text{ cm}$, the diameter will be double of it.
This means the diameter of the circle will be $2r\text{ cm}$.
Therefore, equating the length we get $2r=7.12$.
Now we have to simplify the values.
We divide both sides of the equation with 2 to get $\dfrac{2r}{2}=r=\dfrac{7.12}{2}$.
We multiply 100 to both numerator and denominator to get $r=\dfrac{712}{200}$
We find the simplified form of the fraction $r=\dfrac{712}{200}$.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.
For our given fraction $\dfrac{712}{200}$, the G.C.D of the denominator and the numerator is 2.
Now we divide both the denominator and the numerator with 2 and get $\dfrac{712}{200}=\dfrac{356}{100}=3.56$.

So, the correct answer is “Option B”.

Note: We have to be careful about the unit of the radius where it will be similar to the unit of diameter. We also need to be careful about the position of the decimal of the solution.