Answer:
[tex](a)\ r = 8cm[/tex]
[tex](b\ Area = 200.96cm^2[/tex]
[tex](c)\ Volume = 2143.573cm^3[/tex]
Step-by-step explanation:
The largest cross-section of a sphere is the center.
So, we have:
[tex]A : C = 4 : 1[/tex]
Where
[tex]A = \pi r^2[/tex]
[tex]C =2\pi r[/tex]
Solving (a): The radius
[tex]A : C = 4 : 1[/tex] implies that
[tex]\pi r^2 : 2\pi r = 4 : 1[/tex]
Express as fraction
[tex]\frac{\pi r^2 }{ 2\pi r} = \frac{4 }{ 1}[/tex]
[tex]\frac{\pi r^2 }{ 2\pi r} = 4[/tex]
Divide by [tex]\pi r[/tex]
[tex]\frac{r}{ 2} = 4[/tex]
Make r the subject
[tex]r = 4 * 2[/tex]
[tex]r = 8cm[/tex]
Solving (b): Area of the largest cross-section.
[tex]Area = \pi r^2[/tex]
[tex]Area = 3.14 *8^2[/tex]
[tex]Area = 200.96cm^2[/tex]
Solving (b): Volume of the sphere
[tex]Volume =\frac{4}{3}\pi r^3[/tex]
[tex]Volume =\frac{4}{3} * 3.14 * 8^3[/tex]
[tex]Volume = 2143.573cm^3[/tex]
