Question

# If the radius of a circle is increased by 3 times then the diameter increases by __ times.A. 4B. 6C. 3D. 8

Hint: We can use the relation diameter is 2 times the radius. Then we can take the new radius as 3 times the initial radius. We can apply this new radius in the above relation to get the new diameter. Compare it with the initial diameter to get the required ratio.

Given, the radius of a circle is increased by 3 times.
Let us assume that $r$ is the radius of the circle. Then its diameter twice the radius. It is given by,
$d = 2r$… (1)
Now the radius has increased by 3 times. Let the new radius be $r'$. So, we can write,
$r' = 3r$… (2)
Let the new diameter be $d'$. As the diameter is twice the radius, we can write,
$d' = 2r'$
Using equation (2), we get,
$d' = 2\left( {3r} \right) \\ \Rightarrow d' = 6r \\$
Now we can apply equation (1)
$\Rightarrow d' = 3 \times d$
From the above equation, we can conclude that the increased diameter is 3 times the initial diameter. So, if the radius of a circle is increased by 3 times then the diameter is also increased by 3 times.
Hence, option (C) is correct.

Note: The equation relating the diameter and radius of a circle and simple substitutions are used to solve this problem. Another approach to solving the question would be, We know that $d = 2r$. So, the diameter is directly proportional to the radius. As they have a linear relationship, when the radius increase by n times, the diameter also increases by n times. So, if the radius of a circle is increased by 3 times then the diameter is also increased by 3 times.