1) The surface area available for plants is: S.A = 262,951 m²
2) The volume of of water that could fill the Tianpingmiao tiankeng is:
V = 10,687,698 m³
What is the surface area and volume of the cylinder?
We are given the parameters as:
Diameter: d = 180 m
Thus: radius: r = 180/2 = 90 m
Depth: h = 420 m
1) Formula for surface area of an open cylinder is:
S.A = 2πrh + πr²
where:
r is the radius and h is the height
Plugging in the relevant values gives:
S.A = 2π(90 * 420) + π(90)²
S.A = 262,951 m²
2) Formula for the volume of the open cylinder is:
V = πr²h
Thus:
V = π(90)² * 420
V = 10687698 m³
Complete question is:
A tiankeng is a sinkhole with nearly vertical walls. The Tianpingmiao tiankeng is approximately cylindrical with a diameter of 180
meters and a depth of 420 meters.
a. If the top of the tlankeng is open and plants can grow on the bottom and sides, what is the surface area available for plants? Round to the
nearest square meter.
m²
b. What is the volume of water that could fill the Tianpingmiao tiankeng? Round to the nearest cubic meter.