# Math

Suppose there is a cow that is tied to the corner of a barn with a rope as shown in the
figure below. One side of square barn measures 50 yards
and all the doors on the barn are closed, so the
cow cannot enter the barn (he must walk around the sides only).
How
large of an area
does the co
w have
to walk around and eat
if the length of rope is
1 40 yards
2 75 yards
3 125 yards

1. 👍 0
2. 👎 0
3. 👁 299
1. First one is easy.
The cow can cover 3/4 of a circle with radius 40
(the missing quarter is the barn)
area = (3/4)(π(40^2)
= 1200π yds^2

2nd one:
let's tie the cow up at the top left corner.
with a rope of 75 yds, the cow can cover (3/4)(π(75^2)
or 4218.75π yds^2
Draw an extension of the barn at the top right.
The cow will be able to go 75 yds along that line and then around the corner she can reach the vertical side of the barn 25 yds down that side.
In other words she can cover 1/4 of a smaller circle with radius 25
this will give her an additional (1/4)(π(25^2))
or 156.25π yds^2
But the same will happen at the bottom right corner of the barn
so total area she can cover = 4218.75π + 156.25π +156.25π
= 4531.25π yds^2

3rd one:
I suggest you actually draw in the circles she can cover.
Notice with a rope of 125 yds, the cow can actually come around 2 sides of the barn in either directions and then 25 yds along the third side,
but the radius will change at the corners.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics(Please check)

A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner, as the drawing shows. The centripetal acceleration measured at corner A is n times as great as that

2. ### math

a rectangular pen is to be constructed alongside a barn using 120 feet of fencing. the barn will be used for one side of the pen. What should the dimensions of the pen be to maximize its area. ***Can not use calculus. This is a

3. ### Math

A cow is tethered by a 110-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let a = 10 ft, b = 60 ft, c = 110 ft, d = 70 ft, and e = 60 ft. Round your answer to

4. ### Math

A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed? (Note: The side

1. ### English

11. The speaker of the poem “Your World” goes from living in a small nest in a corner to (1 point) A.being welcomed into a larger flock of birds. B. being devoured by the family’s hungry cat. C.soaring “to the uttermost

2. ### algebra

OLD MCDONALD IS GOING TO PUT A PIG PEN UP AGAINST HIS BARN. HE HAS 45 FEET OF FENCING AND WILL ONLY NEED TO MAKE 3 ADDITIONAL SIDES, AS THE BARN ACTS AS THE FOURTH SIDE.. WHAT IS THE MAXIMUM AREA THAT THE PIG PEN CAN HAVE.

3. ### math

Farmer Hodges has 50 feet of fencing to make a rectangular hog pen beside a very large barn. He needs to fence only three sides because the barn will form the fourth side. Studies have shown that under those conditions the side

4. ### Math

how did farmer john find his missing cow? How did the cow get over the block of hay?

1. ### Complete the two-column proof

Complete the two-column proof Given: triangle SVX is congruent to triangle UTX and Line SV is || to line TU Prove: VUTS is a parallelogram Image: It's a parallelogram, with one line going from corner S to corner U and a line going

2. ### Geometry

A cow is tethered by a piece of rope 50 meters long to the side of a rectangular barn. The rope is fastened to a hook (on the barn) that is located 20 meters from the corner along the longest side of the barn which measures 70

3. ### math

A horse is tied to a post by a rope, 8m long at one corner of a rectangular field. What area of the field can the horse graze? solution pls... tnx...

4. ### AP Lit

What is the significance of Mama remembering having been "hooked in the side by a cow in '49"? A. Like a cow, Mama has a strong spirit and is always ready for a fight. B. Like a cow is mild mannered, Mama is mild mannered and will