A regular hexagonal prism has an edge length 12 cm, and height 10 cm. Identify the volume of the prism to the nearest tenth.

Mathematics

1 answer:

Alexeev081 [22]2 years ago

6 0

Check the picture below.

so the volume will simply be the area of the hexagonal face times the height.

$\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3$

You might be interested in

PLSS HELPP DUE IN 20 MIN. I NEED SOME STEP BY STEP TOO.

Veseljchak [2.6K]

The length of GH is 15.

<h3>How to calculate the length?</h3>

GH = IG

GH = 5x - 10

IG = 3x

5x - 10 = 3x

5x - 3x = 10

2x = 10

x = 10/2 = 5

GH = 5x - 10

= 5 * 5 - 10 = 25 - 10

GH = 15

<ABD = < DBC

<ABD = 10y°

<DBC = (8y + 4)°

10y° = (8y + 4)°

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 4/2 = 2

The value of y is 2

<DBE = <DBC + <CBE

<DBC = 10y°

<CBE = <DBC = 10y°

y = 2

<DBC = <CBE = 10y° = 10*2° = 20°

<DBE = 20° + 20° = 40°

Learn more about angles on:

brainly.com/question/25716982

#SPJ1

8 0

2 years ago

Mark and Tony share a sum of money in the ratio 3:5. What fraction of the money did Tony ratio receive?

gladu [14]

Answer:

Part A is 3/8 of the whole
Part B is 5/8 of the whole

Solution:
Assuming there are no other parts,
the Whole = A + B is the denominator:
Whole = 3 + 5 = 8

Part A = 3 and Part B = 5 are numerators for each fraction.

The fractions are then:
3/8 and 5/8

Meaning:
Part A is 3/8 of the whole
Part B is 5/8 of the whole

4 0

4 years ago

In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of

ira [324]

Answers:
measure angle x = 40°
measure angle y = 35°
measure angle z = 55°

Explanation:
Part (a): getting angle x:
In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°

Part (b): getting angle y:
We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°

Part (c): getting angle z:
In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°

Hope this helps :)