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Alex17521 [72]
3 years ago
11

Use the linear approximation to estimate the change in volume of a right-circular cone of radius r=40 cm if the height is increa

sed from 40 to 41 cm. (Use decimal notation. Give your answer to three decimal places.)
Mathematics
1 answer:
Leviafan [203]3 years ago
7 0

Answer:

The change in volume is 1675.516cm^{3}.

Step-by-step explanation:

The radius of the cone is 40 cm and the height increase from 40 to 41 cm.

dh=41-40\\dh=1

The volume of the cone is,

v=\frac{1}{3}\pi  r^{2}h

Differentiate with respect to h,

\dfrac{dv}{dh} =\dfrac{d}{dh}(\frac{1}{3}\pi  r^{2}h)\\\dfrac{dv}{dh} =\dfrac{1}{3}\pi  r^{2}\frac{dh}{dh}

further simplify as:

\dfrac{dv}{dh} =\dfrac{1}{3}\pi  r^{2}\\dv =\dfrac{1}{3}\pi  r^{2}dh

substitute the value of 1 for  and 40 for r:

dv =\dfrac{1}{3}\pi \times40^{2}\times1\\\\dv =\dfrac{1}{3}\pi \times1600\\\\dv =1675.516

Hence, the change in volume is 1675.516cm^{3}.

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