Question

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)

Answer 1

319.18 square inches of area needed to be painted.

Explanation:

We are given the following in the question:

Diameter of globe = 10.5 inch

`\text{Radius} = \frac{\text{Diameter}}{2} = (10.5)/(2) = 5.25\text{ inch}`

Area that need not be painted = 27 square inches

Surface area of globe =

`\text{Surface area of sphere}\\= 4\pi r^2\\\text{where r is the radius of sphere}\\S = 4* 3.14* (5.25)^2\\S = 346.18\text{ square inches}`

Area to be painted =

`=\text{Surface area of globe - Area that need not be painted}\\= 346.18 - 27\\=319.18\text{ square inches}`

Thus, 319.18 square inches of area needed to be painted.