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3 years ago

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

Mathematics

1 answer:

Maslowich3 years ago

4 0

Answer:

16 pi cubic units

Step-by-step explanation:

Given that a region is bounded by

$f(x)=√x, y=0, x=1, x=4$

And the region is rotated about x axis.

We can find that here radius would be y value and height would be dx

So volume would be as follows:

If f(x) is rotated about x axis volume

= $\pi \int\limits^b_a {y^2} \, dx \\=\pi \int\limits^4_1 {x} \, dx\\=\pi *x^2 ^4_1\\= \pi*16-1\\=15\pi$

cubic units.

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A rectangle sand box has a length of 5 and 1/3 feet and a width of 3 and 3/4 feet. What is the perimeter?

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Answer:

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Step-by-step explanation:

Given:

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Width of the box = $3\frac{3}{4}\ feet$

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Substituting values given for length and width.

Perimeter of sand box = $2(5\frac{1}{3}+3\frac{3}{4})\ feet$

Simplifying by adding fractions:

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⇒ $18\frac{2}{12}$ feet

Simplifying fractions to simplest form.

⇒ $18\frac{1}{6}$ feet

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