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kenny6666 [7]
3 years ago
7

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves x=4y2

−y3 and x=0 about the x-axis.
Mathematics
1 answer:
xenn [34]3 years ago
7 0

Answer = 321.7

Explanation:

radius = y

height = 4y^{2} - y^{3}

area of cylinder = 2π*r*h

Integrate the area to calculate the volume:

= \int\limits^0_4 {2\pi(4y^{3} -y^{4})  } \, dy

= 2\pi (\int\limits^0_4 {4y^{3}dy -\int\limits^0_4  y^{4} dy )} \,

= 2\pi (256-\frac{1024}{5} )

=\frac{512\pi }{5}

= 321.7

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Answer:

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Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

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(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

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mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

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