Calculate the area of a circle with a radius of 2 cm and a circle with a radius of 4 cm. Leave your answers in terms of pi.
When the radius doubles, does the area of the circle double?
A) 4π cm2; 8π cm2; NO
B) 4π cm2; 16π cm2; NO
C) 4π cm2; 16π cm2; YES
D) 4π cm2; 8π cm2; YES
c?
It is B. :)
To calculate the area of a circle, you can use the formula A = πr², where A represents the area and r represents the radius of the circle.
For the circle with a radius of 2 cm:
A = π(2 cm)²
A = π(4 cm²)
A = 4π cm²
For the circle with a radius of 4 cm:
A = π(4 cm)²
A = π(16 cm²)
A = 16π cm²
So, the area of the first circle is 4π cm² and the area of the second circle is 16π cm².
Now, let's examine whether doubling the radius doubles the area.
When we double the radius from 2 cm to 4 cm, the area increases from 4π cm² to 16π cm².
Since the area increased by a factor of 4 (16π divided by 4π), and not by a factor of 2, we can conclude that doubling the radius does not double the area.
Therefore, the correct answer is:
B) 4π cm²; 16π cm²; NO
Not C. doubling 4π gives 8π.
But D is also incorrect.
Note that replacing r with 2r means you have
π(2r)^2 = π*4r^2 = 4πr^2 not 2πr^2