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3 years ago

(Photo) Help meeWhat is the volume of the cone below?

Mathematics

2 answers:

sergejj [24]3 years ago

3 0

Volume = 1/3 pi r^2 h
= 1/3 * 10^2 *81 pi
= 2700 pi units^3

Its C

hram777 [196]3 years ago

3 0

Answer: The correct option is

(C) $2700\pi~\textup{units}^3.$

Step-by-step explanation: We are given to find the volume of the cone in the figure.

We know that the VOLUME of a cone with radius r units and height h units is given by

$V=\dfrac{1}{3}\pi r^2h.$

From the figure, we note that

radius, r = 10 units and height, h = 81 units.

Therefore, the VOLUME of the cone will be

$V\\\\\\=\dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{1}{3}\pi\times 10^2\times 81\\\\\\=27\times 100\pi\\\\=2700\pi~\textup{units}^3.$

Thus, the volume of the cone is $2700\pi~\textup{units}^3.$

Option (C) is CORRECT.

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Read 2 more answers

Use a proof by contradiction to show that the square root of 3 is national You may use the following fact: For any integer kirke

Ierofanga [76]

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1. Let us proof that √3 is an irrational number, using <em>reductio ad absurdum</em>. Assume that $\sqrt{3}=\frac{m}{n}$ where $m$ and $n$ are non negative integers, and the fraction $\frac{m}{n}$ is irreducible, i.e., the numbers $m$ and $n$ have no common factors.

Now, squaring the equality at the beginning we get that

$3=\frac{m^2}{n^2}$ (1)

which is equivalent to $3n^2=m^2$ . From this we can deduce that 3 divides the number $m^2$ , and necessarily 3 must divide $m$ . Thus, $m=3p$ , where $p$ is a non negative integer.

Substituting $m=3p$ into (1), we get

$3= \frac{9p^2}{n^2}$

which is equivalent to

$n^2=3p^2$ .

Thus, 3 divides $n^2$ and necessarily 3 must divide $n$ . Hence, $n=3q$ where $q$ is a non negative integer.

Notice that

$\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}$ .

The above equality means that the fraction $\frac{m}{n}$ is reducible, what contradicts our initial assumption. So, $\sqrt{3}$ is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, $r\in\mathbb{Q}$ , which is equivalent to say that $r=\frac{m}{n}$ where $m$ and $n$ are non negative integers. Also, assume that $k\in\mathbb{Z}$ . So, we want to prove that $k\cdot r\in\mathbb{Z}$ . Recall that an integer $k$ can be written as

$k=\frac{k}{1}$ .

Then,

$k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}$ .

Notice that the product $mk$ is an integer. Thus, the fraction $\frac{mk}{n}$ is a rational number. Therefore, $k\cdot r\in\mathbb{Q}$ .

3. Let us prove by <em>reductio ad absurdum</em> that the sum of a rational number and an irrational number is an irrational number. So, we have $x$ is irrational and $p\in\mathbb{Q}$ .

Write $q=x+p$ and let us suppose that $q$ is a rational number. So, we get that

$x=q-p$ .

But the subtraction or addition of two rational numbers is rational too. Then, the number $x$ must be rational too, which is a clear contradiction with our hypothesis. Therefore, $x+p$ is irrational.

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3 years ago