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)?
_____sq. in.

Answer 1

Answer:

$319.36\text{ inch}^2$

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.

$\text{Area of sphere}=4\pi r^2$, where r represents the radius of sphere.

Since diameter is 2 times the radius, so the radius of our given globe will be:

$r=\frac{10.5}{2}=5.25$

$\text{Area of globe}=4*\pi*5.25^2$

$\text{Area of globe}=4*\pi*27.5625$

$\text{Area of globe}=346.36059$

Since 27 square inches does not need to be painted, so the area we must cover with paint will be:

$346.36059\text{ inch}^2-27\text{ inch}^2=319.36059\text{ inch}^2$

Upon rounding our answer to nearest hundredth we will get,

$319.185\text{ inch}^2\approx 319.36\text{ inch}^2$

Therefore, we must cover 319.36 square inches with paint.

Answer 2

$d=10.5\,\text{in} \\ \\r= \frac{d}{2} = \frac{10.5}{2} =5.25\,\text{in} \\ \\A= 4r^2\pi=4\times5.25^2\pi \approx 346.36 \text{ square inches} \\ \\346.36-27=319.36\text{ square inches}$