If the side of a cylinder is displayed flat instead of as a circle, what shape does it have?
B
b
Divide the surface area of the Earth with the surface area of the Torrid Zone.
A
a
≈ 80.9 million mi^2
B
b
0.41 or 41 %
Practice makes perfect
a
The Torrid Zone is shaped as a 3250 miles wide cylindrical belt around the Earth. This belt, if displayed flat instead of wrapped around the Earth, has the shape of a rectangle.
To find the area of the Torrid Zone we can use the formula for finding the area of a rectangle. The rectangle's length will then be the circumference of the Earth.
A=l w ⇒ A= C_(Earth) w
We find the circumference of the Earth using the formula for the circumference of a circle.
C=2π r
Let's calculate this circumference using that the Earth has a radius of about 3960 miles.
In the exercise we are told that the width of the Torrid Zone is 3250 miles. We can now calculate its surface area.
A= C_(Earth) w
⇓
A= 7920π( 3250)≈ 80.9 million mi^2
b
To find the probability that a meteorite hits in the Torrid Zone we will divide the area of the Torrid Zone with the area of the Earth.
P=A_(Torrid Zone)/A_(Earth)In Part A we used that the surface area of the Torrid Zone is the product of the circumference of the Earth, 2π r, and the width of the Torrid Zone, w.
A_(Torrid Zone)= 2π r* w
To find the surface area of the Earth we will use the formula for the surface area of a sphere.
A_(Earth)= 4π r^2
Let's calculate the probability that a meteorite will land in the Torrid Zone.
