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ch4aika [34]
3 years ago
15

Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
8 0

Answer: 9.6\pi

Step-by-step explanation:

Given

Curve is y=3-3x^2

boundary is y=0 i.e.

\Rightarrow 0=3-3x^2\\\Rightarrow x^2=1\\\Rightarrow x=\pm 1

The volume of solid generated when rotated about the x-axis is

\Rightarrow V=\int_a^b\pi y^2dx

Putting values we get

\Rightarrow V=\int_{-1}^{1}\pi (3-3x^2)^2dx\\\\\Rightarrow V=\int_{-1}^{1}\pi(9+9x^4-18x^2)dx\\\\\Rightarrow V=\pi \left [  \frac{9x^5}{5} - 6 x^3 + 9 x\right ]_{-1}^{1}\\\\\Rightarrow V=9.6\pi

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The area of shaded region.
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Answer:

160π cm²

Step-by-step explanation:

The area of the shaded region is

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A = πr₁² - πr₂²

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r₂ is the radius of the inner circle = 3 cm

A = π × 13² - π × 3²

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3 years ago
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Vesna [10]
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3 years ago
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yuradex [85]

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Step-by-step explanation:

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PLEASE HELP!
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Answer:

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4 years ago
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4 years ago
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