If the radius of a circle is increased by 3 times then the diameter increases by times.

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answer is C.

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Detailed Solution

Concep- We may apply the formula diameter is equal to twice the radius. The new radius may then be calculated as being thrice the original radius. To obtain the new diameter, we may apply this new radius to the relationship mentioned previously. To determine the necessary ratio, compare it to the starting diameter.
Given, a circle's radius is enlarged by three times.
Let's assume that r represents the circle's radius. then double the radius of its diameter. It comes from,

d = 2 r … (1)

Now the radius has increased by 3 times. Let the new radius be

r ′

. So, we can write,

r ′ = 3 r … (2)

Let the new diameter be

d ′

. As the diameter is twice the radius, we can write,

d ′ = 2 r ′

Using equation (2), we get,

d ′ = 2 (3 r)

⇒ d ′ = 6 r

Now we can apply equation (1)

⇒ d ′ = 3 × d

The enlarged diameter is three times the starting diameter, according to the calculation above. In other words, if a circle's radius is tripled, its diameter will likewise be tripled.
Hence, the correct answer is option 3.

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