A stack of 10 quarters is a cylinder. If the diameter of a single quarter is 2.2 cm and the approximate height is 0.17 cm, what is the surface area of a 10-quarter stack?
=6.17
To find the surface area of a 10-quarter stack, we first need to calculate the surface area of a single quarter cylinder and then multiply it by 10.
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr(r + h)
where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of a single quarter is 2.2 cm, we can calculate the radius by dividing the diameter by 2:
Radius (r) = 2.2 cm / 2 = 1.1 cm
The height of a single quarter is approximately 0.17 cm.
Now, we can substitute the values into the formula to find the surface area of a single quarter:
Surface Area of a Single Quarter = 2π(1.1 cm)(1.1 cm + 0.17 cm)
Simplifying this calculation gives us:
Surface Area of a Single Quarter ≈ 2π(1.1 cm)(1.27 cm)
≈ 2.2π(1.27 cm^2)
≈ 8.762 cm^2
Since we have 10 quarters stacked together, we need to multiply the surface area of a single quarter by 10:
Surface Area of a 10-Quarter Stack = 10 * Surface Area of a Single Quarter
≈ 10 * 8.762 cm^2
≈ 87.62 cm^2
Therefore, the surface area of a 10-quarter stack is approximately 87.62 cm^2.
Total height for 10 quarters
h= 0.17*10=1.7cm
Diameter = 2.2 cm, so radius,
r= 1.1 cm
Total surface area (including two ends)
A=2πr²+2πr*h
=2πr(r+h)