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3 years ago

Number 9 need help mathhh

Mathematics

1 answer:

Sergio039 [100]3 years ago

7 0

Using the volume formula, we will see that the volume of the sphere is V = 381.51 cm^3

<h3>How to get the volume of the sphere?</h3>

For a sphere of radius R, the volume is given by the formula:

$V = (\frac{4}{3})*3.14*R^3$

In this case, we can see that the diameter is 9 cm, then the radius is half of that:

R = 9cm/2 = 4.5cm

Now that we know the radius, we can replace it on the volume formula to get:

$V = (\frac{4}{3})*3.14*(4.5cm)^3 = 381.51 cm^3$

If you want to learn more about spheres, you can read:

brainly.com/question/10171109

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A coin is tossed a number cube is rolled <br> P(tails and 3)

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Answer:

1/6

Step-by-step explanation:

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3 years ago

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3 years ago

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V b

Westkost [7]

Explanation:

Let $f(x) = \sqrt{25x}$ and $g(x) = \frac{x^2}{25}$ . The differential volume dV of the cylindrical shells is given by

$dV = 2\pi x[f(x) - g(x)]dx$

Integrating this expression, we get

$\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx$

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

$\sqrt{25x} = \dfrac{x^2}{25}$

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

$25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1$

$x^3 =(25)^3 \Rightarrow x = \pm25$

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

$\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx$