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3 years ago

A cylinder is inscribed in a cube. If the edge of the cube is 3" long, find the volume of the cylinder.

Mathematics

2 answers:

Mazyrski [523]3 years ago

6 0

Answer:

The volume of cylinder is 21.21 units³.

Step-by-step explanation:

The side length of cube is 3 units.

If a cylinder is inscribed in that cube, then radius of the cylinder is 1.5 units and height of the cylinder is 3 units.

The volume of the cylinder is

$V=\pi r^2h$

The volume of cylinder is

$V=\pi \times (1.5)^2\times (3)$

$V=21.20575$

$V\approx 21.21$

Therefore the volume of cylinder is 21.21 units³.

maks197457 [2]3 years ago

4 0

Answer:

21.2 cubic inches

Step-by-step explanation:

Supposing that the diameter of the cylinder match with the longitude of the edge of the cube (see figure attached); then, cylinder's diameter (D) and height (h) are equal to 3 inches.

The volume of the cylinder (V) is calculated as follows:

V = π*(D^2)/4*h

V = π*(3^2)/4*3

V = 21.2 cubic inches

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kramer

Inequalities are used to express unequal expressions.

The inequalities from the word problems are:

$\mathbf{m - 3.5 \le -2}$ .
$\mathbf{0 \ge 2x + 1}$ .
$\mathbf{-\frac 12 \ge 2k - 4}$

The statements from the inequalities are:

-4 is not a solution to $\mathbf{x + 8 < -3}$
-6 is not a solution to $\mathbf{10 \le 3 - m}$
-1 is not a solution to $\mathbf{-3x \le -12.5}$

Graph b represents $\mathbf{x > -7}$

<h3>The word problems</h3>

<u>1. A number minus 3.5 is less than or equal to -2</u>

The statement can be broken down into the following expressions

$\mathbf{A\ number\ minus\ 3.5 \to m - 3.5}$

$\mathbf{less\ than\ or\ equal\ to\ -2 \to \le -2}$

So, when the expressions are brought together, we have:

$\mathbf{m - 3.5 \le -2}$

<u>2. Zero is greater than or equal to twice a number x plus 1</u>

The statement can be broken down into the following expressions

$\mathbf{Zero\ is\ greater\ than\ or\ equal\ to \to 0 \ge }$

$\mathbf{twice\ a\ number\ x\ plus\ 1\ \to 2x + 1}$

So, when the expressions are brought together, we have:

$\mathbf{0 \ge 2x + 1}$

<u />

<u>3. -1/2 is at least twice a number k minus 4</u>

The statement can be broken down into the following expressions

$\mathbf{-\frac 12\ is\ at\ least \to -\frac 12 \ge }$

$\mathbf{twice\ a\ number\ k\ minus\ 4\ \to 2k - 4}$

So, when the expressions are brought together, we have:

$\mathbf{-\frac12 \ge 2k - 4}$

None of the options is correct

<h3>The solutions</h3>

<u>4. Tell whether -4 is a solution to x + 8 < -3</u>

We have:

$\mathbf{x + 8$

Subtract 8 from both sides

$\mathbf{x + 8 - 8$

$\mathbf{x$

The above inequality means that:

-4 is not a solution, because -4 is greater than -11

<u>5. Tell whether -6 is a solution to 10 <= 3 - m</u>

We have:

$\mathbf{10 \le 3 - m}$

Subtract 3 from both sides

$\mathbf{10 -3\le 3 - 3 - m}$

$\mathbf{7 \le - m}$

Multiply both sides by -1 (the inequality sign changes)

$\mathbf{-7 \ge m}$

Make m the subject

$\mathbf{m \le -7}$

The above inequality means that:

-6 is not a solution, because -6 is greater than -7

<u>6. Tell whether -1 is a solution to -3x <= -12.5</u>

We have:

$\mathbf{-3x \le -12.5}$

Divide both sides by -3 (the inequality sign changes)

$\mathbf{x \ge 4\frac16}$

The above inequality means that:

<em>x is greater than or equal to </em> $\mathbf{4\frac16}$ <em />

-1 is not a solution, because -1 is less than $\mathbf{4\frac16}$ <em />

<h3>The graph</h3>

The inequality is given as: $\mathbf{x > -7}$

The less than sign (>) means that:

The graph would use an open circle
The arrow must point to the right

Only graph b satisfies this condition

Hence, the graph of $\mathbf{x > -7}$ is graph b