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*r2
A = 4 * 3.14 * 5.25^2
A = 346.185
346.185 - 27 = 319.185 = 219.19 sq. in.
346.185 - 27 = 319.185 = 319.19 sq. in.
To find the surface area that needs to be covered with paint, we need to subtract the area that does not need to be painted from the total surface area of the globe.
The formula to calculate the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
First, we need to find the radius of the globe. The diameter is given as 10.5 inches, so the radius is half of the diameter:
Radius = Diameter / 2 = 10.5 / 2 = 5.25 inches
Next, we can substitute the value of the radius into the surface area formula:
Surface Area of the Globe = 4π(5.25^2) = 4π(27.5625) ≈ 109.3488 square inches
Finally, we subtract the area that does not need to be painted, which is given as 27 square inches:
Surface Area to be Painted = Surface Area of the Globe - Area that does not need to be painted
≈ 109.3488 - 27 ≈ 82.35 square inches
Therefore, to the nearest hundredth, approximately 82.35 square inches of the globe need to be painted.