The volume of a cone is 36 xin 3. What is the volume of a cylinder with the same base and height as the cone?

Mathematics

1 answer:

mafiozo [28]3 years ago

5 0

Answer: 108 cu. in

Step-by-step explanation:

Area of a cone 1/3 pi r2 h

Area of a cylinder pi r2 h

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Lucy is going to walk in a fundraising event to raise money for her school band. Her mother has agreed to donate $7.50 to the sc

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Step-by-step explanation:

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3 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin(x

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Answer with explanation:

The equation of two curves are

y=8 sin x

y=8 cos x

The point of intersection of two curves are

→8 sin x=8 cos x

sinx = cos x

$x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}$

When you will look between points , 0 and $x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}$ ,the curve obtained is right angled triangle.

Now, rotate the curve that is right angled triangle along the line , y= -1, to obtain a shape similar or resembling with Right triangular prism.

Draw a circular disc in the right triangular prism , having radius =x,and small part on the triangle having length dx.dx varies from 0 to $\frac{\pi}{4}$ .

Required volume of solid obtained

$=\int\limits^{\frac{\pi}{4}}_0 {8 \sin x} \, dx \\\\=|-8\cos x|\left \{ {{x=\frac{\pi}{4}}} \atop {x=0}} \right.\\\\=8-4\sqrt{2}$

=8-4√2 cubic units

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3 years ago

In a certain manufacturing plant, the first operation can be done on any one of five machines, the second operation on only one

Ymorist [56]

Let's see all the steps:
1) operation : 5 options
2) only one option: we ignore it
3) the third operation: 6 options
4): 2 options.

So we have 5 options, 6 options and 2 options: and they are independent of each other. This means that we multiply the numbers, and 5*6*2=60 So the answer is 60!

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3 years ago

Read 2 more answers

If a = √3-√11 and b = 1 /a, then find a² - b²

Serga [27]

If $b=\frac1a$ , then by rationalizing the denominator we can rewrite

$b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8$