Question

PLEASE HELP ASAP, 40 POINTS!!!

Answer 1

D. 256 sq. cm

Explanation:

Given:

• Area of circle = 64 π cm²

To find :

• Area of square =?

Solution:

We have,

Area of circle = π r²

Where, r is radius.

64 π = π r²

Dividing both side by π

`\sf (64\pi)/(\pi)=(\pi r^2)/(\pi)`

64 = r²

Square rooting on both sides

`\sf √(64)=√(r^2)`

We get,

r = 8 cm

Again,

Here,

Diameter is a length of square, so

Diameter = 2* r = 2*8 = 16 cm

Now,

Area of square = length*length

So,

Area of square = 16*16

Area of square = 256 cm².

Therefore,

Answer is D. 256 sq. cm

Answer 2

D. 256 sq. cm

Explanation:

The diagram shows a circle inscribed in a square, where the area of the circle is 64π cm².

As the diameter of the circle is equal to the side length of the square, we can calculate the side length of the square by finding the diameter of the circle.

The formula for the area of a circle is A = πr², where r is the radius.

Given the area of the circle is 64π cm², then the radius (r) is:

`\begin{aligned}\pi r^2&=64\pi\\r^2&=64\\√(r^2)&=√(64)\\r&=8\; \sf cm\end{aligned}`

As the diameter of a circle is twice its radius, the side length of the square is 16 cm.

The area of a square is the square of its side length. Therefore:

`\begin{aligned}\sf Area\;of\;a\;square&=\sf (side\;length)^2\\&=16^2\\&=16 \cdot 16\\&=\rm 256\;sq.\;cm\end{aligned}`

Therefore, the area of the square is 256 sq. cm.