Question

1. Consider a sphere with a radius of 18 inches.

Answer 1

Answer:

1. The surface area is $A=1296\pi \:in^2$ and the volume is $V=7776\pi \:in^3$.

2. The diameter of the sphere is $d=\sqrt{\frac{2463}{\pi }}\approx 27.9999 \:cm$.

Step-by-step explanation:

The surface area of a sphere is given by the formula

                                                   $A=4\pi r^2$

The volume enclosed by a sphere is given by the formula

                                                  $V=\frac{4}{3}\pi\cdot r^3$

where $r$ 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

$A=4\pi \left(18\right)^2\\\\A= 4\cdot \:324\pi\\\\A=1296\pi \:in^2$

and the volume is

$V=\frac{4}{3}\pi \left(18\right)^3=\frac{4\pi 18^3}{3}=\frac{3^6\cdot \:2^3\cdot \:4\pi }{3}=7776\pi \:in^3$

2. The diameter of a sphere is given by $d=2r$, where $r$ 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.

$A=4\pi r^2\\\\2463=4\pi r^2\\\\4\pi r^2=2463\\\\r^2=\frac{2463}{4\pi }\\\\r=\frac{\sqrt{2463}\sqrt{\pi }}{2\pi }\approx13.99997 \:cm$

and the diameter is

$d=2\cdot \frac{\sqrt{2463}\sqrt{\pi }}{2\pi }=\sqrt{\frac{2463}{\pi }}\approx 27.9999 \:cm$