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Talja [164]
3 years ago
11

he radius of a right circular cylinder is increasing at a rate of 7.5 inches per minute and the height is decreasing at a rate o

f 13.5 inches per minute. What is the rate of change of the surface area when the radius is 15.5 inches and the height is 33 inches
Mathematics
1 answer:
Pani-rosa [81]3 years ago
8 0

Answer:Rate of change of the surface area =876.85 square inches

Step-by-step explanation:

Surface area of a cylinder=2*pie*radius*height

Former radius and height are 8.0inches(15.5-7.5) and 46.5inches(33+13.5) respectively

New radius and height are 15.5inches and 33 inches respectively.(pie 22/7)

2*22*8*46.5=16368/7=2338.29

Also 2*22*15.5*33=22506/7=3215.14

Rate of change is 3215.14-2338.29=876.85inches

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<u>ANSWER</u>

{r}^{2}  = 4  \cos2\theta

<u>EXPLANATION</u>

The Cartesian equation is

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We substitute

x = r \cos( \theta)

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This implies that

{( {r}^{2} )}^{2}  = 4(( { r \cos\theta)  }^{2} -  {(r \sin\theta) }^{2}  )

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Factor the RHS to get:

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Divide through by r²

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