Question

Help pleaseeeee. Tyyy

Answer 1

Answer:

Option B.

Step-by-step explanation:

The measure of cage is 90 feet by 40 feet.

Length of rope $=40\sqrt{2}$ foot

It is clear that, length of rope is greater than one side of cage and raw a line which divides the cage in two parts as shown in below figure.

We need to find the shaded area.

By Pythagoras theorem:

$hypotenuse^2=base^2+perpendicular^2$

$(40\sqrt{2})^2=(40)^2+perpendicular^2$

$3200=1600+perpendicular^2$

$3200-1600=perpendicular^2$

$1600=perpendicular^2$

$40=perpendicular$

So, it is a square.

From the figure it is clear that the shaded area contains 1/8th part of circle are half part of square.

Area of circle is

$A_1=\pi r^2$

$A_1=\pi (40\sqrt{2})^2$

$A_1=3200\pi$

Area of square is

$A_2=a^2$

$A_2=(40)^2$

$A_2=1600$

Area of shaded portion is

$A=\dfrac{A_1}{8}+\dfrac{A_2}{2}$

$A=\dfrac{3200\pi}{8}+\dfrac{1600}{2}$

$A=400\pi+800$

$A=400(\pi+2)$

The required area is $400(\pi+2)$ sq. ft.

Therefore, the correct option is B.