Answer :
[tex]d=10.5\,\text{in}
\\
\\r= \frac{d}{2} = \frac{10.5}{2} =5.25\,\text{in}
\\
\\A= 4r^2\pi=4\times5.25^2\pi \approx 346.36 \text{ square inches}
\\
\\346.36-27=319.36\text{ square inches}[/tex]
Answer:
[tex]319.36\text{ inch}^2[/tex]
Step-by-step explanation:
We have been given that we need to paint the globe held aloft by a statue of Atlas. Its diameter is 10.5 in.
First of all we will find the area of globe using area of sphere formula.
[tex]\text{Area of sphere}=4\pi r^2[/tex], where r represents the radius of sphere.
Since diameter is 2 times the radius, so the radius of our given globe will be:
[tex]r=\frac{10.5}{2}=5.25[/tex]
[tex]\text{Area of globe}=4*\pi*5.25^2[/tex]
[tex]\text{Area of globe}=4*\pi*27.5625[/tex]
[tex]\text{Area of globe}=346.36059[/tex]
Since 27 square inches does not need to be painted, so the area we must cover with paint will be:
[tex]346.36059\text{ inch}^2-27\text{ inch}^2=319.36059\text{ inch}^2[/tex]
Upon rounding our answer to nearest hundredth we will get,
[tex]319.185\text{ inch}^2\approx 319.36\text{ inch}^2[/tex]
Therefore, we must cover 319.36 square inches with paint.