With
expected El Nino weather conditions around the corner, scientists
are concerned about the future of the Great Barrier Reef, referred
to as the world’s largest living organism. If the reef’s area
(133,300 square miles) was perfectly arranged in a square region,
its perimeter would measure x miles. If the reef’s area was
arranged in a circular region, its circumference would measure y
miles. What is the value of x - y? Express your answer to the
nearest whole number.
Solution
To
find the perimeter of a square region with area 133,300 square
miles, we perform the following operations: sqrt(133,300) = 365.1
(which is the length of one side of the square) and 365.1×4 =
1460.41 miles = x. To find the circumference of a circular region
with area 133,300 square miles, we perform the following operations:
133,300÷pi = 42,430.708 (which is equal to the radius-squared) and
sqrt(42,430.708) = 205.987 miles (which is equal to the radius) and
therefore the circumference = (pi)(2)(205.987) = 1294.2555 = y.
Subtracting y from x, we see the difference is 166, to the nearest
whole mile.
Problem
The evergreen shrubs at Mr. Green's nursery are
planted in rows on a square plot of land measuring 2401 square feet.
The shrubs are planted in such a manner that the centers of the
shrubs are 7 feet apart and the outer shrubs are planted along the
edges of the plot, with a shrub at each corner. Mr. Green spent $896
to cover all the costs necessary for raising this crop of
evergreens.If
Mr. Green succeeds in selling each shrub for $35, his profit will be
what percent of his total cost?
Solution
Mr. Green's profit is 150% of his total cost.
By finding the square root of 2401, you can
determine that the plot of land measures 49 feet by 49 feet. With
shrubs planted along the edges and at the corners of the plot, with
7 feet between each shrub, there is room for 8 rows, each with 8
shrubs, for a total of 64 shrubs. So, Mr. Green's total selling
price is 64 x $35 = $2240.
His profit equals the total selling price less the total cost
to produce the shrubs, so Mr. Green's profit will be $2240 - $896 =
$1344.
To write $1344 (his profit) as a percent of $896
(his total cost), you can write it first as a fraction or as a
decimal, and then multiply by 100: 1344/896 = 1.5 or 150%.
