Find the surface area and lateral area of the following three prisms. Be sure to show all of your work.
Answers
Problem 1
L = 10 = length
W = 5 = width
H = 4 = height
SA = surface area of a rectangular prism, aka block or box
SA = 2*(LW+LH+WH)
SA = 2*(10*5+10*4+5*4)
SA = 220
--------------------
LA = lateral area, aka wall area
LA = (perimeter of the base)*(height)
LA = (2L+2W)*H
LA = (2*10+2*5)*4
LA = 120
or
LA = SA - (floor area) - (ceiling area)
LA = SA - 2*(area of the floor)
LA = 220 - 2*(LW)
LA = 220 - 2*(10*5)
LA = 220 - 100
LA = 120
--------------------
Answers:
Surface Area = 220 square feet
Lateral Area = 120 square feet
==========================================================
Problem 2
Imagine rotating the object so that the triangular face is resting on the flat ground. This means the triangular faces are the floor and ceiling. The walls of any prism are always rectangles.
Focus on the right triangle with leg b = 4 and hypotenuse c = 5.
Use the pythagorean theorem to find that a = 3 is the missing leg length.
The triangle has base = 4 and height = 3, so its area is base*height/2 = 4*3/2 = 6 square inches. This is the area of the floor and ceiling each.
--------------------
This is the summary so far
base or floor area = 6 square inchesdepth of the prism = 8 inches(a,b,c) = (3,4,5) are the sides of the right triangleThose values are then plugged into the formulas below.
SA = surface area of a triangular prism
SA = 2*(base area) + depth*(a+b+c)
SA = 2*(6) + 8*(3+4+5)
SA = 108
LA = lateral area
LA = depth*(a+b+c)
LA = 8*(3+4+5)
LA = 96
or
LA = SA - 2*(floor area)
LA = 108 - 2*(6)
LA = 96
Note that a+b+c = perimeter of the triangular base.
--------------------
Answers:
Surface Area = 108 square inches
Lateral Area = 96 square inches
==========================================================
Problem 3
Imagine rotating the figure so that the octagon is resting on the flat ground.
Refer to the screenshot below to see the steps on computing the area of the regular octagon, aka the floor area.
The floor area is approximately 120.710678 square cm. The same goes with the ceiling because the floor and ceiling are congruent regular octagons that are parallel.
Each rectangular wall has an area of 5*22 = 110 square cm. Eight identical walls give a total lateral area of 8*110 = 880 square cm.
Add the floor and ceiling area to the wall area to get the total surface area
floor + ceiling + walls = 120.710678 + 120.710678 + 880 = 1121.421356
--------------------
Answers:
Surface Area = 1121.421356 square cm (approximate)
Lateral Area = 880 square cm
Related Questions
Which statements can be used to compare the characteristics of the functions? select two options. f(x) has an all negative domain. g(x) has the greatest maximum value. all three functions share the same range. h(x) has a range of all negative numbers. all three functions share the same domain.
Answers
The statements that can be used to compare the characteristics of the functions are:
g(x) has the maximum greatest value.h(x) has a range of all negative numbers.How to interpret the functions?From the table of values (see attachment), we have the following highlights:
f(x) has a range of all positive numbers.h(x) has a range of all negative numbers.g(x) has the maximum greatest value.The above highlights mean that, the true statements are b and d
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Answer:Its B,D
Step-by-step explanation: Yes
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Answers
Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
Solving :
(2 cos(θ))² = 2
4 cos²θ = 2
cos²θ = 1/√2
cosθ = [tex]\frac{\pi }{4}[/tex]
4cos^2θ=2
cos^2θ=1/2
cosθ= ±√(1/2)
θ= π/4 and 3π/4
So the smallest answer is π/4
At the end of the winter, coats are on sale for 75% off. If a heavy coat was priced
at $120 after taking the discount, then how much will the coat ring up for at the register
if the tax is 6%?
Answers
Answer:
the answer is $31.80
Step-by-step explanation:
6% of $120.00 is $7.20,
75% off of 127.20= $31.80
There are 26 counters in a bag. 5 of the counters are pink. 10 of the counters are blue. the rest of the counters are white. jan puts some more pink counters into the bag. she then takes some blue counters out of the bag. after she has done this there are still 26 counters in the bag. jan then takes at random a counter from the bag. the probability that she takes a pink counter is 1/2 what is the probability that she takes a blue counter?
Answers
The probability of picking a blue counter from the bag is 1 / 13.
What is the probability?The number of counters initially in the bag:
white counters = 26 - 10 - 5 = 11 pink counters = 5 blue counters = 10The number of counters now in the bag:
white counters = 11pink counters = (5 + x) / 26 = 1/213/26
x = 13 - 5 = 8
blue counters = 26 - 13 - 11 = 2Probability of picking a blue counter = number of blue counters / total number of counters
2/26 = 1 / 13
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b) The mean of 7, 5, 0, 1, 3, 4 and h is 10. Find the value of h.
Answers
Step-by-step explanation:
mean =10
sum of no =7+5+0+1+3+4+h=20+h
N=7
now
mean=sum of no/N
10=20+h/7
10×7=20+h
70-20=h
h=50
How many minutes per week do the students in our class play video games please help
Answers
Answer:
Mean: 599, Median 60
Step-by-step explanation:
0,0,0,14,16,30,60,260,300,420,1500,2592,2595
add them all up it gives you 7,787 divided by the number of numbers(13) to find the mean.
Mean: 599
Sort them from smallest to greatest and the number directly in the middle is the median.
Median: 60
I'm having a little trouble with it,
Answers
Answer:
Each person received 3 slices and 3 are left
Answer:
D) Each person receives 3 slices, and there are 3 slices left over
Step-by-step explanation:
If each pizza was cut into 8 slices, then there were 3*8=24 slices.
If we attempt to share 24 slices with 7 people, there would be 3 slices for each person, with 3 left over since 7*3=21, and 21+3=24.
Write an 27, 31, 35, .... explicit formula for an, the n th term of the sequence
Answers
Answer :
See below ~
Explanation :
Common difference (d) between terms is :31 - 27 = 4Then the recursive formula is :
aₙ = aₙ₋₁ + 4Desmis Unit 7 Practice Day 1
Answers
The number of unique triangle can be formed using the angles 30 degrees, 90 degrees and 100 degrees is 0.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
The measure of angles are given as,
A 90 degree angleA 100 degree angleA 30 degree angleTo create a triangle with these angles, the sum should be equal to 180 degree of three angles.
90+100+30 > 180
90+90+30 > 180
90+90+100 > 180
100+100+30 > 180
30+100+30 < 180
30+90+30 < 180
There is no combination of angles, which is equal to the 180 degree.
Hence, the number of unique triangle can be formed using the angles 30 degrees, 90 degrees and 100 degrees is 0.
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PLS HELP!!!!!!!! GEOMETRIC SEQUENCE!!!!!
Answers
Answer:
-256
Step-by-step explanation:
The numbers are being multiplied by 2.
( -4 * 2 = -8)
(-8* 2 = -16)
A cable extends from the top of a radio tower to a point 360 feet from the base of the tower. If the
cable is 850 feet long, how tall is the tower?
Answers
Step-by-step explanation:
we have a right-angled triangle :
the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.
then the ground distance (360 ft) and the height of the tower are the 2 legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse.
in our case
850² = 360² + height²
height² = 850² - 360² = 592,900
height = 770 ft
the tower is 770 ft tall.
Answer:
770 feet
Step-by-step explanation:
Given
Cable = 850 feet longExtends from radio tower to a point 360 feet from the base of a towerSolving
Using the Pythagorean Theorem, we can find the height(distance from base)² + (height)² = (length of cable)²height² = (850)² - (360)²height² = 722,500 - 129,600height² = 592,900height = √592,900height = 770 feetSelect the table that represents a linear function.
Answers
Answer: C.
Step-by-step explanation: In a linear function, both numbers rise or fall in a steady way. This means the answer would be c, where the x rises in increments of one, and y increases by multiplying by three each time.
If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints?
If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints? A. 48 ft^2 B. 64 ft^2 C. 96 ft^2 D. 112 ft^2
the measurements are 4,4,6 and 3
Answers
Answer:
^2D its because the shed has only two faces
Corresponding Angles are congruent. Which angle corresponds with
Answers
Answer:
Angle<8 corresponds with angle<3
Step-by-step explanation:
Corresponding angles are congruent and are on the same side of the transversal. They occupy corresponding positions. So,
Angle 1 and Angle 6 are corresponding angles
Angle 3 and Angle 8 are corresponding angles
Angle 2 and Angle 5 are corresponding angles
Angle 4 and Angle 7 are corresponding angles
Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores a 70 or below? Use the formula for a z-score z = x - mu/infinity where x is the given value, mu is the mean and infinity is the standard deviation. Then refer to the chart on page 11 of the lesson to find the probability. a. .0668.b. .0179.c. .0013.d. .5000.
Answers
The probability that the student scores a 70 or below is 0.0013
How to determine the probability?The given parameters are:
Mean, μ = 82Standard deviation, σ = 4The probability that a student scores 70 or below is represented as:
P(x ≤ 70)
Calculate the z score for x = 70 using:
[tex]z =\frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z =\frac{70 - 82}{4}[/tex]
Evaluate
z =-3
The probability becomes
P(x ≤ 70) = P(z ≤ -3)
Using the z tables of probabilities, we have:
P(x ≤ 70) = 0.0013499
Approximate
P(x ≤ 70) = 0.0013
Hence, the probability that the student scores a 70 or below is 0.0013
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the perimeter of a rhombus whose sides are 12 units in length is:
48
144
192
Answers
Answer:
48
Step-by-step explanation:
12*4=48
the quotient of a and b
Answers
Step-by-step explanation: and that should give you your answer and if not please feel free to mesage me.
Angle relationships with parallel lines
Answers
Answer:
x = 132
Step-by-step explanation:
x = 180 - 48
x = 132
x=180-48
x=132
describe the end behavior of f(x)=2x^3
Answers
Answer:
as x→+∞, f(x)→+∞ as x→-∞,f(x)→-∞
Step-by-step explanation:
HELP ME OUT NO SCAM OR ELSE!!!! I ONLY GOT 1 MIN!!!! 50 BRAINLY PTS
Answers
Answer:
The two middle ones
Step-by-step explanation:
9. Find the midpoint of the segment having endpoints (4.1,−6.6) and (6.6,−4.1).
Answers
Answer: [tex]\displaystyle (5.35, -5.35)[/tex]
Step-by-step explanation:
We will use the midpoint formula. See attached or view below.
What does this formula do? We are, essentially, finding the average for the x-values and y-values.
[tex]\displaystyle (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )[/tex]
[tex]\displaystyle (\frac{4.1+6.6}{2}, \frac{-6.6+-4.1}{2} )[/tex]
[tex]\displaystyle (\frac{10.7}{2}, \frac{-10.7}{2} )[/tex]
[tex]\displaystyle (5.35, -5.35)[/tex]
PLLLLEASE help- geometry
Answers
Answer: Reflection, translation
Step-by-step explanation:
WILL GIVE BRAINLIEST PLEASE HELP ASAP
Please answer this in word form and do it fast because I’m running out of time. Will give brainliest
Answers
Step-by-step explanation:
because the distance from O to the other 3 points is the same. each bisector provides a line of points with equal distance to the 2 end points of its base line.
where these 2 bisectors intersect, is the point that has the same distance to all end points.
samantha got home after school and found a package sitting on the front porch she carried 20N package upstairs her stair are 10m tall how much work did she do (need to show solution)
Answers
Answer:
Zero
Step-by-step explanation:
Work done in the vertical direction is 0 because no displacement can be taken. Hence, the correct answer to this problem is zero
PLEASE HELP!!!!!!!!!!!!!
Answers
no lo sé, pero como necesito puntos, ¿sí?
Which ratio table below does not represent a proportional relationship between the number of laptop and desktop computers being sold at an electronics store?
Answers
Answer:
table 1
Step-by-step explanation:
a table represents a proportional relationship between the number of laptop and desktop computers ,if the ratio of the number of desktop computers to laptops is a constant (doesn’t vary)
Table1 : (does not represent a proportional relationship) because :
11÷10=1,1
46÷42=1.09...
and 1.1 ≠ 1.09
Table2 : (represents a proportional relationship) because :
3÷6=0.5
9÷18=0.5
18÷36=0.5
72÷144=0.5
Table3 : (represents a proportional relationship) because :
18÷12=1.5
36÷24=1.5
54÷36=1.5
108÷72=1.5
Table4 : (represents a proportional relationship) because :
2÷3=0.666666666667
18÷27=0.666666666667
22÷33=0.666666666667
200÷300=0.666666666667
The richter scale measures the magnitude, m, of an earthquake as a function of its intensity, i, and the intensity of a reference earthquake, . which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? a. b. c. d.
Answers
The magnitude of an earthquake with an intensity 10,000 times is [㏒10000]
What is magnitude?magnitude can be regarded as the size or the weight of destruction that is been experienced as a result of the earthquake.
The magnitude as regards Richter scale is
[㏒(I/I₀]
But we were given l as 10000I₀.
Then if we substitute we have, [㏒(10000I₀./I₀)]
If we simplify we have:
[㏒10000]
Therefore, magnitude of an earthquake with an intensity 10,000 times is [㏒10000]
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PLSS ANSWER!!!
In the circle, O is the center. The radius of the circle is 6 feet. Find the area of the shaded
sectors. Round to the nearest hundredth
Answers
12.57
Step-by-step explanation:
Area = πr²
40/360 × 22/7 × 36
1/9 × 22/7 × 36
(22 × 4)/7 = 12.57
(rounding) 17.23. whats the nearest tenth?
Answers
Answer:
17.2
Step-by-step explanation:
23 ⇒ Below 5, round down
20 ⇒ Add to decimal
17. 23 ⇒ 17.2 / 17.20
find an ordered pair for 4 solution for -5x+y=6
Answers
⇒ Choose three values for [tex]x[/tex] and substitute in to find the corresponding [tex]y[/tex] values.
[tex](0,6),(1,11),(2,16)[/tex]