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3 years ago

What is the volume of a cylinder with the base radius of 10 units and a height of nine units?

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

8 0

Answer:

The volume is $2827.4units^3$ to the nearest tenth

Step-by-step explanation:

The volume of cylinder is : $V=\pi r^2h$

The base radius of the cylinder is r=10 units.

The height of the cylinder is h=9 units.

Substitute the values into the formula to get;

$V=\pi \times 10^2\times 9$

$V=900\pi units^3$

$V=2827.4units^3$ to the nearest tenth

Otrada [13]3 years ago

7 0

Answer:

$V = 2827.43\ units^3$ or $V = 900\pi\ units^3$

Step-by-step explanation:

The volume of a cylinder is calculated by the following formula

$V = \pi r^2 *h$

Where r is the radius of the cylinder and h is the height

In this case we know that the radius r of the base is:

$r=10\ units$

and

$h=9\ units$

So the Volume is:

$V = \pi (10)^2 *9$

$V = 900\pi\ units^3$

$V = 2827.43\ units^3$

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3 years ago

Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

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Answer: The correct line is

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Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

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