A Susan B. Anthony dollar coin has a diameter of 26.50 millimeters. What is the area of the coin to the nearest hundredth?

Question

Emery Allen · Accepted Answer

#551.55 mm^2#

Coin's diameter is 26.50 millimetres

using the unit of measurement of #mm# for millimetres

So its radius is #1/2xx26.50 = 13.25mm#

Area of a circle is #pixx("radius")xx("radius") -> pi("radius")^2#

So the area is #pixx13.25xx13.25#

Using a calculator this is: 551.54586....

For the nearest hundredth we have the cut off point:

#551.54color(red)(|)586...# #" "color(red)(uarr)# #color(red)("cut off point")#

The digit immediately to the right of the cut of point is classified as 5 or more. So the digit to the left of the cut off point is raised by 1 and all those to the right made into 0

#551.55color(red)(|)000..# #" "color(red)(uarr)# #color(red)("The 4 changed to 5")#

Roman Alvarez · Answer

undefined To find the area of the Susan B. Anthony dollar coin, we use the formula for the area of a circle: Area = π * radius^2. The diameter of the coin is 26.50 millimeters, so the radius is half of that, which is 13.25 millimeters. Substituting this radius into the formula, we get: Area ≈ π * (13.25)^2. Using π ≈ 3.14, we calculate the area to be approximately 550.98 square millimeters. Rounded to the nearest hundredth, the area is 550.98 square millimeters.