Answer:
1. The surface area is [tex]A=1296\pi \:in^2[/tex] and the volume is [tex]V=7776\pi \:in^3[/tex].
2. The diameter of the sphere is [tex]d=\sqrt{\frac{2463}{\pi }}\approx 27.9999 \:cm[/tex].
Step-by-step explanation:
The surface area of a sphere is given by the formula
[tex]A=4\pi r^2[/tex]
The volume enclosed by a sphere is given by the formula
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]
where [tex]r[/tex] is the radius of the sphere.
1. From the information given we know that the sphere has a radius of 18 inches.
The surface area is
[tex]A=4\pi \left(18\right)^2\\\\A= 4\cdot \:324\pi\\\\A=1296\pi \:in^2[/tex]
and the volume is
[tex]V=\frac{4}{3}\pi \left(18\right)^3=\frac{4\pi 18^3}{3}=\frac{3^6\cdot \:2^3\cdot \:4\pi }{3}=7776\pi \:in^3[/tex]
2. The diameter of a sphere is given by [tex]d=2r[/tex], where [tex]r[/tex] is the radius of the sphere.
We know that the surface area is 2463 square centimeters. To find the diameter of the sphere first we need to find the the radius.
[tex]A=4\pi r^2\\\\2463=4\pi r^2\\\\4\pi r^2=2463\\\\r^2=\frac{2463}{4\pi }\\\\r=\frac{\sqrt{2463}\sqrt{\pi }}{2\pi }\approx13.99997 \:cm[/tex]
and the diameter is
[tex]d=2\cdot \frac{\sqrt{2463}\sqrt{\pi }}{2\pi }=\sqrt{\frac{2463}{\pi }}\approx 27.9999 \:cm[/tex]
