Find the volume of the regular hexagonal pyramid if the lateral edge is 15 feet.
Answers
Answer:
Volume of the given pyramid = 1122.37 cubic feet
Step-by-step explanation:
Volume of the regular hexagonal pyramid = [tex]\frac{1}{3}(\text{Area of the base})(\text{Base})[/tex]
Measure of internal angle of a polygon = [tex]\frac{(n-2)\times 180}{n}[/tex]
Here, n = number of sides of the polygon
For a hexagon, n = 6
Measure of interior ∠C = [tex]\frac{(6-2)\times 180}{6}[/tex]
= 120°
Measure of ∠BCD = [tex]\frac{120}{2}[/tex]
= 60°
By applying tangent rule in ΔCED,
tan(∠ECD) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(60°) = [tex]\frac{DE}{CE}[/tex]
[tex]\sqrt{3}=\frac{DE}{6}[/tex]
DE = [tex]6\sqrt{3}[/tex] feet
And cos(60°) = [tex]\frac{EC}{CD}[/tex]
[tex]\frac{1}{2}=\frac{6}{CD}[/tex]
CD = 12 feet
Area of ΔBCD = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(6\sqrt{3})(12)[/tex]
= [tex]36\sqrt{3}[/tex] feet
Area of hexagonal Base of the pyramid = [tex]6(36\sqrt{3})[/tex]
= 216√3 square feet
Since, lateral height of the pyramid (AC) = 15 feet
By applying Pythagoras theorem in ΔADC,
AC² = AD² + CD²
(15)² = AD² + (12)²
AD = [tex]\sqrt{225-144}[/tex]
AD = 9 feet
Volume of the given pyramid = [tex]\frac{1}{3}(216\sqrt{3})(9)[/tex]
= 648√3 cubic feet
= 1122.37 cubic feet
Related Questions
What is the volume for this triangular prism if the base of the triangle is 8 the height is 16 and the height for the triangle is 7
Answers
Answer:
Volume of the triangular prism = 448 cm³
Step-by-step explanation:
Volume of the triangular prism = Area of the triangular base × Height of the triangular prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(8)(16)[/tex]
= 64 units²
Volume of the triangular prism = 64 × 7
= 448 cm³
Help please, I'm stuck on this
Answers
An swer:
d
Step-by- step explana tion:
20 points!!!!
Find the area of the regular hexagon. Round to the nearest hundredth.
A)
27.71 in 2
B)
83.14 in?
C)
166.26 in?
D)
332.55 in 2
Answers
Answer: b or a
Step-by-step explanation:
Use the Change of Base Formula to evaluate the expression. Then convert it to a logarithm in base 8. Round to the nearest thousandth if necessary.
log4 8
0.667; log8 4.003
0.301; log8 1.870
1.5; log8 22.627
0.15; log8 1.366
Answers
Answer
1.5; log8 22.627
Step-by-step explanation:
If 2 inches is about 5 centimeters,
about how many inches is 45
centimeters?
Answers
Answer:
about 18 (17.7)
Step-by-step explanation:
Answer:
About 17 inches
Step-by-step explanation:
PLEASE HELP ME WITH THIS I WILL GIVE BRAINLIEST
Answers
Answer:
12, 24, and 60
Please help it‘a due today
Answers
Answer:
u know area of rectangle is length × breadth
therefore, area = (3x+4)×(7x-2)
= 21x²-6x+28x-8
= 21x²+22x-8
= d ans
for brainiest:):):):):):):)
Answers
6. 6.28
7. 21.98
8. 94.2
what is the value of x
Answers
Answer:
The value of x is dependant on the value of y.
Step-by-step explanation:
y = (number)x + (another number)
I need a PNG or picture to give you a factual answer to the value of X.
the length of AC to the nearest hundredth is ____
Answers
Answer:
5.41
Step-by-step explanation:
Find the perimeter of a circle with radius 35cm.[Takex=[22/7}]
Answers
Answer:
i have made it in above picture
220 cm
hope it helps
Find the measure of each angle indicated.
23°
128°
Answers
Find the acute angle in the first quadrant used as a reference for
23, 128, 337, 128
help anyone? please?
Answers
Answer:
x=11.2
Step-by-step explanation:
Set up a proportion:
x+11/36 = 37/60
Cross multiply:
1332=60(x+11)
Distribute:
1332=60x+660
Subtract 660 from 1332
672=60x
Divide:
x=11.2
I'm not sure if this is the correct answer but I hope this helps! :)
Correct me if I'm wrong!
what is the m<R???????
Answers
Answer:
128
Step-by-step explanation:
Hey There!
So the rule about interior angles of a trapezoid
is that the angles that lie on the segments that are not parallel are supplements
so essentially what I'm saying is that angle R and angle U are supplementary angles so to find x we do
180=15x+8+7x-4
step 1 combine like terms
15+7=22
8-4=4
now we have
180=22x+4
step 2 subtract 4 from each side
180-4=176
now we have
176=22x
step 3 divide each side by 22
176/22=8
so x=8
now we plug in 8 to 15x+8
8x15=120
120+8=128
so we can conclude that angle R = 128
what are some expressions that are equivalent to 6(m+2+ m)
Answers
Answer:
12m + 12 is one equivalent expression
Step-by-step explanation:
This can be found by distributing the numbers as shown below:
6(m + 2 + m)
6m + 12 + 6m
12m + 12
Awnser:
The awnser would be 8m in total.
You could do 4(m +4 m) or 8(m+0 m) or 3(m +5 m)4x – 5.2y + 6y + 7.9x – 8x *
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{4x - 5.2y + 6y + 7.9x - 8x}[/tex]
[tex]\huge\text{COMBINE your LIKE TERMS}[/tex]
[tex]\large\textsf{(4x + 7.9x - 8x) + (-5.2y + 6y)}[/tex]
[tex]\large\textsf{4x + 7.9x - 8x =}[/tex]
[tex]\large\textsf{4x + 7.9x = 11.9x}[/tex]
[tex]\large\textsf{11.9x - 8x = 3.9x}[/tex]
[tex]\large\textsf{4x + 7.9x - 8x = 3.9x}[/tex]
[tex]\large\textsf{(3.9x) + (-5.2y + 6y)}[/tex]
[tex]\large\textsf{-5.2y + 6y = 0.8y}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf3.9x + 0.8y }}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
3.9x+0.8y
Step-by-step explanation:
4x−5.2y+6y+7.9x−8x
Combine −5.2y and 6y to get 0.8y.
4x+0.8y+7.9x−8x
Combine 4x and 7.9x to get 11.9x.
11.9x+0.8y−8x
Combine 11.9x and −8x to get 3.9x.
3.9x+0.8y
It can also be converted to fraction form:
[tex]\frac{4y}{5}+\frac{39x}{10} = 3.9x+0.8y[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
(ILL GIVE BRAINLY)
Answers
Answer:
um... what are trying to say?
Step-by-step explanation:
Answer:
Step-by-step explanation:
∠H is congruent to ∠B
:::::
GH/DJ = AB/DC
If the time now is 4 PM on Saturday, after 253 hours the time will be:
(A) Sun. 5AM
(B)Tues. 5AM
(C) Wed. 1AM
(D) Wed. 5AM
Answers
Answer:
C I'm pretty sure
Step-by-step explanation:
Pls help and thank you so much
Answers
Answer:
y=4x+3
Step-by-step explanation:
y intercept is 3 and x is 4
a boy has $5 coins and a $10 coins they are eight coins all together and their value is $55 how many of each kind does he have
Answers
Answer:
3 $10 coins and 5 $5 coins
Step-by-step explanation:
The area of the rectangular-shaped lot is 44,075 square feet. The width of the lot is 215 feet. How long is the lot the Mitchells are looking to buy?
Answers
Answer:
205 feet
Step-by-step explanation:
44075/215= 205
can u guys help me i need help on this question
Answers
Answer: 6p=120
Step-by-step explanation:
Explanation:
P must be isolated because that is what you would solve for.
120 is our total & must be divide by the number of pieces (p’s) that make up 120
Therefore you have p = 120/6
Hope that explains well, I am not a math teacher
Solve the equation.
3x + 2(4x − 6) = 8x + 1
Please help :) also have a good day :D
What is the value for x?
Please enter fractional values in the form ‘a/b’. For example, an answer of [tex]\frac{1}{3}[/tex] will be entered as 3/4.
x =
Answers
Answer:
3x + 2(4x − 6) = 8x + 1
3x + (8x-12)=8x+1
-12=19x+1
-11=19x
-11/19 (Im pretty sure i did this right but at the same time im not, im sorry if i got this wrong)
Answer:
=13/3
Step-by-step explanation:
1. Distribute
3+2(4−6)=8+1
3+8−12=8+1
2. Combine like terms
3+8−12=8+1
11−12=8+1
3. Add 12 to both sides of the equation
11−12=8+1
11−12+12=8+1+12
4. Simplify
11=8+13
5. Subtract 8x from both sides of the equation
11=8+13
11−8=8+13−8
6. Simplify
3=13
7. Divide both sides of the equation by the same term
3=13
3x÷3=13÷3
8. Simplify
If you cancel terms that are in both the numerator and denominator you will get:
=13/3
I hope this helps
7 of 10
© Brian invests £990 into his bank account. He receives 2% per year simple interest. How much
will Brian have after 4 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
1071.61
Step-by-step explanation:
That's how much
I WILL MARK BRAINLIEST IF GOTTEN RIGHT!!!!!!!
Answers
Answer:
a I don't know I just guess I hope you got it right I hope
885 = 5(x + 19)
what is x?
Answers
Answer:
x = 158
Step-by-step explanation:
Given
885 = 5(x + 19) ← divide both sides by 5
177 = x + 19 ( subtract 19 from both sides )
158 = x
Answer: x=158
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Luke wants to send 21 parcels by the Express service.
He does the calculation 20 x £15 = £300 to estimate the cost.
(b)
Explain why Luke's calculation shows the actual cost will be more than £300
Answers
Answer:
Because he has to send one more parcel than the estimation.
Step-by-step explanation:
Use the Distributive Property to simplify the expression. 11(b−3)
Answers
Answer: 11b-33
Step-by-step explanation:
did this help
Hello.
In order to simplify the given expression, we need to use the Distributive Property, which states
a(b+c)=ab+ac.
So let's simplify it! :)
Multiply 11 times b and -3:
[tex]\Large\boxed{11b-33}[/tex]
I hope it helps.
Have an outstanding day. :)
[tex]\boxed{imperturbability}[/tex]
if 36/5x=3/5 what is x
Answers
Answer:
x = 12
Step-by-step explanation:
Given
[tex]\frac{36}{5x}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
15x = 180 ( divide both sides by 15 )
x = 12
SOMEONE PLEASE HELP ME...
If k=
[tex] log_{2}(3) [/tex]
Rewrite
[tex] log_{2}(48) [/tex]
in terms of k.
Answers
9514 1404 393
Answer:
k+4
Step-by-step explanation:
48 = 16×3 = 2^4×3
log2(48) = log2(2^4) +log2(3)
log2(48) = 4 + k