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The surface area of this sphere is 615.44 square yards. What is the volume of this sphere? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

 Oct 8, 2020
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The surface area of this sphere is 615.44 square yards. What is the volume of this sphere? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.   

 

The first thing to do is determine the radius of the sphere 

We'll just use the formula for the area of a sphere                            4 π r2  =  A

Area is 615.44 and 4 π is 12.56 so plug them in                         (12.56) r2  =  615.44  

 

Divide both sides by 12.56                                                                       r2  =  49  

 

Well.  That turned out pretty convenient.  A perfect square. 

 

Take the square root of both sides.                                                            r  =  7 

Actually it's +7 but we discard the negative value. 

 

                                                                                                           4  

Now use the formula to determine the volume of a sphere.       V  =  –– π r3    

                                                                                                           3  

 

Doing a little arithmetic on the calculator                                             4308.08

                                                                                                  V  =  ——–——  

                                                                                                                 3   

 

Once more to the calculator and ta da                                       V  =  1436.03 yd3   

.

 Oct 8, 2020

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