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Chapter 3: Q. 4 (page 313)

Volume and Surface Area Formulas: Write a formula for (a) the volume and (b) the surface area of each solid described below.

A sphere of circumferenceC.

Short Answer

Expert verified

(a) Volume of the sphere with circumference Cis,V=C36蟺2

(b) Surface area of the sphere with circumference Cis,role="math" localid="1648564459714" A=C2蟺

Step by step solution

01

Part (a) step 1. Given information  

We have to find the volume and surface area of the given figure.

For that, we have been given a sphere of circumference C.

The formula to find the circumference isC=2蟺谤, where ris the radius.

Therefore,

The radius of the sphere,role="math" localid="1648564371660" r=C2蟺...........(1)

02

Part (a) step 2. The volume of the sphere  

The formula to find the volume of the sphere is, V=43蟺谤3

By substituting the value of rin the formula we get,

V=4蟺3C2蟺3=4蟺颁33脳8脳蟺3=C36蟺2

The volume of the sphere with circumference C isV=C36蟺2.

03

Part (b) step 3. The surface area of the sphere 

The formula to find the surface area of the sphere is,S=4蟺谤2

By substituting the value of rin the formula we get,

localid="1648564340687" S=4蟺C2蟺2=4蟺C24蟺2=C2蟺

The surface area of the sphere with circumference C is V=C2蟺.

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Most popular questions from this chapter

Determine whether or not each function fsatisfies the hypotheses of the Mean Value Theorem on the given interval [a,b]. For those that do, use derivatives and algebra to find the exact values of all c鈭�(a,b)that satisfy the conclusion of the Mean Value Theorem.

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