Mathematics
Lovegirk33
5

Your classmate claims that if you double the radius of a sphere, its surface area and volume will quadruple. What is your classmate’s error? Explain.

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(1) Answers
bridjetestrada

SA of a sphere is 4πr²   Using a sample of radius 3 the SA would be 36π² (4πx3²)   If we double the radius and make it 6, the SA would be 144π² So for Surface area, your classmate is correct. What about the volume?  V of a Sphere = 4/3 π r³ Again using 3 the Volume of a Sphere with radius 3 = 4/3 π 27 But the volume of a sphere with radius 6 = 4/3 π 216 which is eight times the volume of the smaller sphere. (27 x 8 =216)  So your friend is right about Surface Area but wrong about the volume.

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