http://mathworld.wolfram.com/PentagonalPrism.html
http://easycalculation.com/area/learn-penta-prism.php
A right pentagonal prism is 10 cm high. If the area of each pentagonal base is 32 cm squared and the perimeter is 20 cm, what are the lateral and total surface areas of the prism?
I tried doing this using the formula shown in my book, but it came out wrong. the formula I was using was for a triangular prism. What the heck is the formula for a pentagonal prism?
22 answers
triangular prism ---> base is a triangle
pentagonal prism ---> base is a pentagon
So clearly you can't use the triangular prism formula for this question , but you an generalize it looking what it describes.
I don't know what they gave you, but the surface area of a triangular prism consists of
2 congruent triangular bases + 3 congruent rectangles
so the surface area of a pentagon
= 2 (area of the pentagon) + 5rectangles
you are given that the perimeter is 20, so each side of the base is 20/5 = 4, and the height is 10
so the surface area of the 5 rectangles is 5(4)(10) = 200
add the 2 pentagon areas of 32 each for a total of
200 + 64 = 264 cm^2
your text should give you the definitions of lateral and total surface areas, make the necessary adjustments.
pentagonal prism ---> base is a pentagon
So clearly you can't use the triangular prism formula for this question , but you an generalize it looking what it describes.
I don't know what they gave you, but the surface area of a triangular prism consists of
2 congruent triangular bases + 3 congruent rectangles
so the surface area of a pentagon
= 2 (area of the pentagon) + 5rectangles
you are given that the perimeter is 20, so each side of the base is 20/5 = 4, and the height is 10
so the surface area of the 5 rectangles is 5(4)(10) = 200
add the 2 pentagon areas of 32 each for a total of
200 + 64 = 264 cm^2
your text should give you the definitions of lateral and total surface areas, make the necessary adjustments.
Thank you, that makes more sense than what I tried.
its wrong srry
The pentagonal prism below has a base area of 38 units
2
2
and a volume of 368.6 units
3
3
. Find its height.
2
2
and a volume of 368.6 units
3
3
. Find its height.
Let the height of the pentagonal prism be "h" and let the length of one of the sides of a regular pentagon base be "s".
First, we can use the formula for the area of a regular pentagon to find s:
Area of a regular pentagon = (5/4) * s^2 * cot(pi/5)
38 = (5/4) * s^2 * cot(pi/5)
s^2 = 38 * 4 / (5 * cot(pi/5))
s^2 ≈ 12.969
s ≈ 3.6
Now, we can use the formula for the volume of a pentagonal prism to solve for h:
Volume of a pentagonal prism = (5/2) * s^2 * h * cot(pi/5)
368.6 = (5/2) * (3.6)^2 * h * cot(pi/5)
h ≈ 10.9
Therefore, the height of the pentagonal prism is approximately 10.9 units.
First, we can use the formula for the area of a regular pentagon to find s:
Area of a regular pentagon = (5/4) * s^2 * cot(pi/5)
38 = (5/4) * s^2 * cot(pi/5)
s^2 = 38 * 4 / (5 * cot(pi/5))
s^2 ≈ 12.969
s ≈ 3.6
Now, we can use the formula for the volume of a pentagonal prism to solve for h:
Volume of a pentagonal prism = (5/2) * s^2 * h * cot(pi/5)
368.6 = (5/2) * (3.6)^2 * h * cot(pi/5)
h ≈ 10.9
Therefore, the height of the pentagonal prism is approximately 10.9 units.
The pentagonal prism below has a base area of 45 units
2
2
and a height of 10.3 units. Find its volume.
2
2
and a height of 10.3 units. Find its volume.
The volume of a pentagonal prism is given by the formula:
V = (5/2) * base area * height
Therefore, the volume of the given pentagonal prism is:
V = (5/2) * 45 * 10.3 = 1158.75 cubic units
Therefore, the volume of the pentagonal prism is 1158.75 cubic units.
V = (5/2) * base area * height
Therefore, the volume of the given pentagonal prism is:
V = (5/2) * 45 * 10.3 = 1158.75 cubic units
Therefore, the volume of the pentagonal prism is 1158.75 cubic units.
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Alonso sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
349 visitors purchased no costume.
71 visitors purchased exactly one costume.
12 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
349 visitors purchased no costume.
71 visitors purchased exactly one costume.
12 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The total number of visitors to the website in a single day is given by:
Total = 349 + 71 + 12 = 432
The probability that the next person will purchase no costume is the number of visitors who purchased no costume divided by the total number of visitors. So, we have:
Probability of purchasing no costume = 349/432
Converting this to a percentage and rounding to the nearest whole number, we get:
Probability of purchasing no costume = 80%
Therefore, the probability that the next person will purchase no costume is 80%.
Total = 349 + 71 + 12 = 432
The probability that the next person will purchase no costume is the number of visitors who purchased no costume divided by the total number of visitors. So, we have:
Probability of purchasing no costume = 349/432
Converting this to a percentage and rounding to the nearest whole number, we get:
Probability of purchasing no costume = 80%
Therefore, the probability that the next person will purchase no costume is 80%.
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 9
Blue 14
Green 11
Yellow 7
Purple 9
Based on these results, express the probability that the next spin will land on red or blue or yellow as a percent to the nearest whole number.
Spinner Results
Color Frequency
Red 9
Blue 14
Green 11
Yellow 7
Purple 9
Based on these results, express the probability that the next spin will land on red or blue or yellow as a percent to the nearest whole number.
The total number of spins is:
9 + 14 + 11 + 7 + 9 = 50
The probability of the next spin landing on red or blue or yellow is the sum of the number of red, blue, and yellow sections divided by the total number of sections on the spinner. Therefore, we have:
Probability of landing on red or blue or yellow = (9 + 14 + 7) / 50
Simplifying:
Probability of landing on red or blue or yellow = 30/50
Converting this to a percentage and rounding to the nearest whole number, we get:
Probability of landing on red or blue or yellow = 60%
Therefore, the probability of the next spin landing on red or blue or yellow is 60%.
9 + 14 + 11 + 7 + 9 = 50
The probability of the next spin landing on red or blue or yellow is the sum of the number of red, blue, and yellow sections divided by the total number of sections on the spinner. Therefore, we have:
Probability of landing on red or blue or yellow = (9 + 14 + 7) / 50
Simplifying:
Probability of landing on red or blue or yellow = 30/50
Converting this to a percentage and rounding to the nearest whole number, we get:
Probability of landing on red or blue or yellow = 60%
Therefore, the probability of the next spin landing on red or blue or yellow is 60%.
Find the volume of a pyramid with a square base, where the side length of the base is
17
in
17 in and the height of the pyramid is
9
in
9 in. Round your answer to the nearest tenth of a cubic inch.
17
in
17 in and the height of the pyramid is
9
in
9 in. Round your answer to the nearest tenth of a cubic inch.
The formula for the volume of a pyramid is:
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
Substituting the given values, we get:
base area = 17 in * 17 in = 289 in^2
Now, we can use the formula for the volume of a pyramid to solve for the volume:
V = (1/3) * base area * height = (1/3) * 289 in^2 * 9 in ≈ 867.0 in^3
Rounding to the nearest tenth of a cubic inch, we get:
V ≈ 867.0 in^3
Therefore, the volume of the pyramid is approximately 867.0 cubic inches.
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
Substituting the given values, we get:
base area = 17 in * 17 in = 289 in^2
Now, we can use the formula for the volume of a pyramid to solve for the volume:
V = (1/3) * base area * height = (1/3) * 289 in^2 * 9 in ≈ 867.0 in^3
Rounding to the nearest tenth of a cubic inch, we get:
V ≈ 867.0 in^3
Therefore, the volume of the pyramid is approximately 867.0 cubic inches.
Find the volume of a pyramid with a square base, where the area of the base is
14.4
ft
2
14.4 ft
2
and the height of the pyramid is
9.6
ft
9.6 ft. Round your answer to the nearest tenth of a cubic foot.
14.4
ft
2
14.4 ft
2
and the height of the pyramid is
9.6
ft
9.6 ft. Round your answer to the nearest tenth of a cubic foot.
The formula for the volume of a pyramid is:
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
We need to find the side length of the square base with an area of 14.4 ft^2:
14.4 ft^2 = side length * side length
Taking the square root of both sides, we get:
side length = √14.4 ft ≈ 3.8 ft
Now that we know the base area and the height, we can substitute these values into the formula for the volume of a pyramid:
V = (1/3) * base area * height = (1/3) * 14.4 ft^2 * 9.6 ft ≈ 43.5 ft^3
Rounding to the nearest tenth of a cubic foot, we get:
V ≈ 43.5 ft^3
Therefore, the volume of the pyramid is approximately 43.5 cubic feet.
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
We need to find the side length of the square base with an area of 14.4 ft^2:
14.4 ft^2 = side length * side length
Taking the square root of both sides, we get:
side length = √14.4 ft ≈ 3.8 ft
Now that we know the base area and the height, we can substitute these values into the formula for the volume of a pyramid:
V = (1/3) * base area * height = (1/3) * 14.4 ft^2 * 9.6 ft ≈ 43.5 ft^3
Rounding to the nearest tenth of a cubic foot, we get:
V ≈ 43.5 ft^3
Therefore, the volume of the pyramid is approximately 43.5 cubic feet.
Find the volume of a pyramid with a square base, where the perimeter of the base is
8.6
cm
8.6 cm and the height of the pyramid is
8.1
cm
8.1 cm. Round your answer to the nearest tenth of a cubic centimeter.
8.6
cm
8.6 cm and the height of the pyramid is
8.1
cm
8.1 cm. Round your answer to the nearest tenth of a cubic centimeter.
For a pyramid with a square base, the perimeter of the base can be calculated as:
perimeter = 4 * side length
We can use this to find the side length of the square base:
4 * side length = 8.6 cm
side length = 2.15 cm
Now that we know the side length and the height, we can use the formula for the volume of a pyramid:
V = (1/3) * base area * height
The base area for a square base with side length 2.15 cm is:
base area = side length * side length = (2.15 cm)^2 ≈ 4.6225 cm^2
Substituting the values for the base area and height, we get:
V = (1/3) * 4.6225 cm^2 * 8.1 cm ≈ 12.6935 cm^3
Rounding to the nearest tenth of a cubic centimeter, we get:
V ≈ 12.7 cm^3
Therefore, the volume of the pyramid is approximately 12.7 cubic centimeters.
perimeter = 4 * side length
We can use this to find the side length of the square base:
4 * side length = 8.6 cm
side length = 2.15 cm
Now that we know the side length and the height, we can use the formula for the volume of a pyramid:
V = (1/3) * base area * height
The base area for a square base with side length 2.15 cm is:
base area = side length * side length = (2.15 cm)^2 ≈ 4.6225 cm^2
Substituting the values for the base area and height, we get:
V = (1/3) * 4.6225 cm^2 * 8.1 cm ≈ 12.6935 cm^3
Rounding to the nearest tenth of a cubic centimeter, we get:
V ≈ 12.7 cm^3
Therefore, the volume of the pyramid is approximately 12.7 cubic centimeters.
Find the volume of a pyramid with a square base, where the side length of the base is
16.6
m
16.6 m and the height of the pyramid is
9.1
m
9.1 m. Round your answer to the nearest tenth of a cubic meter.
16.6
m
16.6 m and the height of the pyramid is
9.1
m
9.1 m. Round your answer to the nearest tenth of a cubic meter.
The formula for the volume of a pyramid is:
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
Substituting the given values, we get:
base area = 16.6 m * 16.6 m = 275.56 m^2
Now, we can use the formula for the volume of a pyramid to solve for the volume:
V = (1/3) * base area * height = (1/3) * 275.56 m^2 * 9.1 m ≈ 830.6 m^3
Rounding to the nearest tenth of a cubic meter, we get:
V ≈ 830.6 m^3
Therefore, the volume of the pyramid is approximately 830.6 cubic meters.
V = (1/3) * base area * height
For a pyramid with a square base, the base area can be calculated as:
base area = side length * side length
Substituting the given values, we get:
base area = 16.6 m * 16.6 m = 275.56 m^2
Now, we can use the formula for the volume of a pyramid to solve for the volume:
V = (1/3) * base area * height = (1/3) * 275.56 m^2 * 9.1 m ≈ 830.6 m^3
Rounding to the nearest tenth of a cubic meter, we get:
V ≈ 830.6 m^3
Therefore, the volume of the pyramid is approximately 830.6 cubic meters.
The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th.
Score Number of Students
60
60
2
2
65
65
1
1
70
70
2
2
75
75
2
2
80
80
4
4
85
85
5
5
90
90
3
3
Score Number of Students
60
60
2
2
65
65
1
1
70
70
2
2
75
75
2
2
80
80
4
4
85
85
5
5
90
90
3
3
To find the mean score, we need to calculate the sum of all the scores and divide by the total number of students.
To do this, we can multiply each score by the number of students who received that score, then add up the products, and divide by the total number of students:
(60 * 2) + (65 * 1) + (70 * 2) + (75 * 2) + (80 * 4) + (85 * 5) + (90 * 3) = 2110
There are a total of 19 students, so:
mean score = 2110 / 19 ≈ 111.05
Rounding to the nearest tenth, we get:
mean score ≈ 111.1
Therefore, the mean score is approximately 111.1.
To do this, we can multiply each score by the number of students who received that score, then add up the products, and divide by the total number of students:
(60 * 2) + (65 * 1) + (70 * 2) + (75 * 2) + (80 * 4) + (85 * 5) + (90 * 3) = 2110
There are a total of 19 students, so:
mean score = 2110 / 19 ≈ 111.05
Rounding to the nearest tenth, we get:
mean score ≈ 111.1
Therefore, the mean score is approximately 111.1.
2 answers