A metal washer 1 in. in diameter is pierced by a 1/2-in. hole. What is the area of one face of the washer?
for a circle, A = πr^2
you have two circles, so find the difference in their areas.
YAWA
To find the area of one face of the washer, we need to find the area of the circular shape. The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Given that the diameter of the washer is 1 inch, we can find the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2
Radius (r) = 1 inch / 2
Radius (r) = 0.5 inches
Now we can substitute the value of the radius into the formula:
A = π * r^2
A = π * (0.5 inches)^2
A = π * 0.25 square inches
So, the area of one face of the washer is π * 0.25 square inches.
To find the area of one face of the washer, we need to first find the area of the full circle and then subtract the area of the hole.
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the diameter of the washer is 1 inch, we can find the radius by dividing the diameter by 2. Therefore, the radius (r) of the washer is 1/2 inch.
Now we can calculate the area of the full circle using the formula:
A = π(1/2)^2
A = π(1/4)
A = π/4
So, the area of the full circle is π/4 square inches.
Next, we need to find the area of the hole. The hole has a diameter of 1/2 inch, so the radius (r) of the hole is 1/4 inch.
Using the same formula, we can calculate the area of the hole:
A_hole = π(1/4)^2
A_hole = π(1/16)
A_hole = π/16
Therefore, the area of the hole is π/16 square inches.
Finally, to find the area of one face of the washer, we subtract the area of the hole from the area of the full circle:
A_face = A - A_hole
A_face = (π/4) - (π/16)
A_face = (4π - π)/16
A_face = (3π)/16
So, the area of one face of the washer is (3π)/16 square inches.