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The circumference of a sphere was measured to be 89 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in thecalculated surface areaPreviewEstimate the relative error in the calculated surface area.PreviewGet help: Video

Question
The circumference of a sphere was measured to be 89 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the
calculated surface area
Preview
Estimate the relative error in the calculated surface area.
Preview
Get help: Video
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The circumference of a sphere was measured to be 89 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area Preview Estimate the relative error in the calculated surface area. Preview Get help: Video

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Step 1

Circumference of a sphere with radius r is,

С 3 2лr
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С 3 2лr

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Step 2

Differentiating with respect to r, we get

dC2T
dr
When Ar is small, we can write
AC2T
Ar
AC
Ar
27T
Given that AC 0.5 cm
0.5
.. Ar
27T
1
Ar
47T
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dC2T dr When Ar is small, we can write AC2T Ar AC Ar 27T Given that AC 0.5 cm 0.5 .. Ar 27T 1 Ar 47T

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Step 3

Now consider the surface area of the sphere and ...

S 4Tr2
dSSTr
dr
When Ar is small, we can write
AS
877r
Ar
AS 87r- Ar
AS 4-2Tr Ar
( C 27Tr)
AS 4C-Ar
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S 4Tr2 dSSTr dr When Ar is small, we can write AS 877r Ar AS 87r- Ar AS 4-2Tr Ar ( C 27Tr) AS 4C-Ar

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Tagged in

Math

Calculus

Derivative

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