Question

Eliza paints a circle on her bedroom wall as part of a mural. After she paints it, she decides that she wants a much bigger circle. So, she multiplies her original radius by four and repaints the circle. Which statement best describes Eliza's solution?
a.) The area of the new circle is two times larger.

b.) The area of the new circle is four times larger.

c.) The area of the new circle is eight times larger.

d.) The area of the new circle is 16 times larger.

Answer 1

Answer: d.) The area of the new circle is 16 times larger.

Step-by-step explanation:

Let the radius of the original circle be r.

Then the area of the original circle will be :-

$\text{A}_1=\pi r^2$

When she multiplies her original radius by four and repaints the circle.

The new radius = $R=4r$

Then the area of the new circle will be :-

$\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1$

Hence, The area of the new circle is 16 times larger.

Answer 2

D. the area of the new circle is 16 times larger

Hope this helps :)