Question

Help pleaseeeee. Tyyy

Answer 1

Option B.

Explanation:

The measure of cage is 90 feet by 40 feet.

Length of rope
`=40√(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√(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√(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=(A_1)/(8)+(A_2)/(2)`

`A=(3200\pi)/(8)+(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.