Question

: If the radius of a circle is tripled, the area becomes
A.9 times
B.3 times
C.6 times
D.30 times

Answer 1

Hint: Find the ratios of the area of the circle with tripled ratio to the area of the normal circle.Find the area of of smaller circle and bigger circle by using the formula given for area of the circle, from the formula it is evident that area is directly proportional to the radius of the circle.

Complete step-by-step answer:

A circle is a round shaped figure that has no corners or edges; it is also defined as a closed, two dimensional curved shape whose all points in a plane are at equal distance from a point called center. The distance between any points of the circle is equal and this length is called radius.
The area is defined as the space occupied by a flat shape or surface by an object on a two-dimensional plane. The area of a figure is the number of unit square space that it covers, generally expressed in square centimeter or square meter.

Let the radius of the circle be \[x\]
The area of the circle is given as \[A = \pi {r^2}\]
Therefore the area of the circle will be
\[
  A = \pi {r^2} \\
   = \pi {x^2} \\
 \]
Now it is said that the radius of the circle is tripled hence the new radius
\[r' = 3x\]
So the area of the new circle will be
\[
  A' = \pi {\left( {r'} \right)^2} \\
   = \pi {\left( {3x} \right)^2} \\
   = 9\pi {x^2} \\
 \][Since\[r' = 3x\]]
Now, since \[A = \pi {x^2}\]
Hence we can write,
\[
  A' = 9\pi {x^2} \\
  A' = 9 \\
  \dfrac{{A'}}{A} = 9 \\
 \]
Therefore we can say that the area becomes 9 times when the radius of the circle is tripled.
So, the correct answer is “Option A”.

Note: Students must note that the area of a circle is directly dependent upon its square time of the radius hence if the radius is increased or decreased n times then its area will change n square times.