Question

Use SOLVEM steps for the following problem.

Suppose that the earth is a smooth sphere and you could wrap a 25,000 mile band snugly around it. If you lengthen the band by 6 feet, what would be the largest animal that can fit under the new band (assuming the band is equally above the earth's surface)?

a) an amoeba

b) a 3 inch diameter snake

c) a 1 foot high opossum

d) a 1.5 foot high alligator

e) a 5 foot 11 inch tall person



Note: make sure you keep your units consistent! Circumference = Pi * Diameter

5280 feet in a mile, Pi ~ 3.14159

radius = Diameter/2

Show your work!

Answer 1

C = So the largest animal that can fit under the new band is a 1 foot high opossum, which is smaller than the maximum height of 12,072,001 feet + 6 inches.

Step-by-step explanation:

C = Pi * D = Pi * 25,000 miles

Converting this to feet, we get:

C = Pi * 25,000 miles * 5280 feet/mile = Pi * 132,000,000 feet

Adding 6 feet to the length of the band gives us:

C' = C + 6 feet = Pi * 132,000,000 feet + 6 feet

The new circumference is still the same distance from the center of the Earth as the original circumference, so we can use the formula for the circumference of a circle to find the radius of the circle that the band now forms:

C' = Pi * 2 * r

Solving for r, we get:

r = C' / (2 * Pi) = (Pi * 132,000,000 feet + 6 feet) / (2 * Pi)

Simplifying this expression, we get:

r = 66,000,003 feet / 2 = 33,000,001.5 feet

Now we can find the largest animal that can fit under the band by finding the maximum height of an animal that can fit under a circle with this radius.

Maximum height = r - radius = 33,000,001.5 feet - 20,928,000 feet = 12,072,001.5 feet

Converting this to feet and inches, we get:

Maximum height = 12,072,001.5 feet = 12,072,001 feet + 0.5 feet

= 12,072,001 feet + 6 inches

Answer 2

c) a 1 foot high opossum

Step-by-step explanation:

SOLVEM Steps:

S = State the problem

O = Organize the information

L = Label the variables

V = Verify the problem

E = Establish a strategy

M = Manipulate the variables

S: Suppose that the earth is a smooth sphere and you could wrap a 25,000 mile band snugly around it. If you lengthen the band by 6 feet, what would be the largest animal that can fit under the new band (assuming the band is equally above the earth's surface)?

O:

Original circumference = 25,000 miles

Additional length = 6 feet

L:

Let's label the radius of the earth as r, and the height of the animal as h.

V:

The problem seems to be well-formed and makes sense.

E:

We can use the original circumference of the earth to find its radius, and then calculate the new circumference by adding the extra 6 feet to the length of the band. Then we can solve for the maximum height of the animal that can fit under the new band.

M:

Convert the original circumference to feet:

C = 25,000 * 5280 feet/mile = 132,000,000 feet

Calculate the original radius of the earth:

C = 2πr

r = C / (2π) = 132,000,000 / (2 * 3.14159) = 21,008470.23 feet

Calculate the new circumference:

C_new = C + 6 feet = 132,000,006 feet

Calculate the new diameter and radius:

d_new = C_new / π = 42,016,942.38 feet

r_new = d_new / 2 = 21,008,471.19 feet

Calculate the maximum height of the animal:

h = r_new - r = 21,008,471.19 - 21,008470.23 feet=0.96 feet

If answer is 0.96 feet, the largest animal that can fit under the new band (assuming the band is equally above the earth's surface) would be a 1 foot high opossum (option c).