You are to paint the globe held aloft by a statue of Atlas. Its diameter is 10.5 in. How much surface area must you cover with paint if 27 square inches does not need to be painted (to the nearest hundredth)?
Surface area = 4 pi r 2
A = 4 * 3.14 * 5.25^2
A = 4 * 3.14 * 27.5625
A = 346.105 square inches
Subtract 27 from the total.
To find the surface area of the globe that needs to be painted, we can use the formula for the surface area of a sphere:
Surface Area = 4πr²
Where r is the radius of the sphere.
Given that the diameter of the globe is 10.5 inches, we can determine the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 10.5 inches / 2 = 5.25 inches
Substituting this value into the formula for surface area:
Surface Area = 4π(5.25)²
Calculating the surface area of the globe:
Surface Area ≈ 346.36 square inches
Since 27 square inches do not need to be painted, we subtract this value from the total surface area:
Area to be painted = Total Surface Area - Area not to be painted
Area to be painted ≈ 346.36 square inches - 27 square inches
Area to be painted ≈ 319.36 square inches (rounded to the nearest hundredth)
Therefore, you need to cover approximately 319.36 square inches of the globe's surface with paint.