Imagine you have two similar triangular pyramids. The volume of the smaller triangular pyramid is 343 cm³ and the volume of the larger one is 729 cm³. What is the scale factor of the smaller figure to the larger figure?(1 point) Responses
5:9
11:20
1:14
7:9
11 answers
5:9
Question 1: Sketch the region enclosed by the lines x=0, x=5, y=3 and y=8. Revolve the region around the y-axis. Identify the solid formed by the revolution(1 point) Responses
Cylinder
Sphere
Cone
Pyramid
Question 2: Calculate the volume of the solid described above. Round your answer to the nearest whole number
Cylinder
Sphere
Cone
Pyramid
Question 2: Calculate the volume of the solid described above. Round your answer to the nearest whole number
Answer to Question 1: Cylinder
Answer to Question 2: The volume of the cylinder formed by revolving the region around the y-axis can be calculated using the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius is 5 units (since the region extends from x=0 to x=5), and the height is 5 units (as the difference between y=3 and y=8).
Therefore, V = π(5^2)(5) = 125π ≈ 393 cubic units. Rounded to the nearest integer, the volume of the cylinder is 393 cubic units.
Answer to Question 2: The volume of the cylinder formed by revolving the region around the y-axis can be calculated using the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius is 5 units (since the region extends from x=0 to x=5), and the height is 5 units (as the difference between y=3 and y=8).
Therefore, V = π(5^2)(5) = 125π ≈ 393 cubic units. Rounded to the nearest integer, the volume of the cylinder is 393 cubic units.
15. The lateral area of a cone is 572 π cm^2. The radius is 20. Find the slant height to the nearest tenth. (1 point) Responses
26.3 cm 26.3 cm
20.4 cm 20.4 cm
28.6 cm 28.6 cm
22.6 cm
26.3 cm 26.3 cm
20.4 cm 20.4 cm
28.6 cm 28.6 cm
22.6 cm
To find the slant height of the cone, you can use the formula for the lateral area:
Lateral Area of a Cone = π * r * l, where r is the radius and l is the slant height.
Given:
Lateral Area = 572π cm²
Radius (r) = 20 cm
Now, plug in these values and solve for l:
572π = π * 20 * l
572 = 20l
l = 572 / 20
l = 28.6 cm
Therefore, the slant height of the cone is 28.6 cm.
The correct response provided is: 28.6 cm.
Lateral Area of a Cone = π * r * l, where r is the radius and l is the slant height.
Given:
Lateral Area = 572π cm²
Radius (r) = 20 cm
Now, plug in these values and solve for l:
572π = π * 20 * l
572 = 20l
l = 572 / 20
l = 28.6 cm
Therefore, the slant height of the cone is 28.6 cm.
The correct response provided is: 28.6 cm.
Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom and sides of the cylinder. The diameter of each ball is 18 cm.
a. What is the volume of the cylinder rounded to the nearest tenth?
b. What is the total volume of the three balls rounded to the nearest tenth?
Show all work to receive full points.
a. What is the volume of the cylinder rounded to the nearest tenth?
b. What is the total volume of the three balls rounded to the nearest tenth?
Show all work to receive full points.
Since each ball just touches the top, bottom, and sides of the cylinder, the diameter of the balls is equal to the height of the cylinder. Therefore, the diameter = height = 18 cm.
a. Volume of the cylinder:
The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height (in this case, diameter).
Given:
Diameter = 18 cm
Radius (r) = 18/2 = 9 cm
Height (h) = Diameter = 18 cm
V = π * 9^2 * 18
= π * 81 * 18
= 1458π cm³
Rounded to the nearest tenth, the volume of the cylinder is approximately 4591.6 cm³.
b. Volume of one sphere:
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius.
Radius of the ball = diameter/2 = 18/2 = 9 cm
Total volume of one ball:
V_ball = (4/3)π * 9^3
= (4/3) * 729π
= 972π cm³
Total volume of the three balls:
V_total = 3 * V_ball
= 3 * 972π
= 2916π cm³
Rounded to the nearest tenth, the total volume of the three balls is approximately 9162.3 cm³.
a. Volume of the cylinder:
The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height (in this case, diameter).
Given:
Diameter = 18 cm
Radius (r) = 18/2 = 9 cm
Height (h) = Diameter = 18 cm
V = π * 9^2 * 18
= π * 81 * 18
= 1458π cm³
Rounded to the nearest tenth, the volume of the cylinder is approximately 4591.6 cm³.
b. Volume of one sphere:
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius.
Radius of the ball = diameter/2 = 18/2 = 9 cm
Total volume of one ball:
V_ball = (4/3)π * 9^3
= (4/3) * 729π
= 972π cm³
Total volume of the three balls:
V_total = 3 * V_ball
= 3 * 972π
= 2916π cm³
Rounded to the nearest tenth, the total volume of the three balls is approximately 9162.3 cm³.
It doesn't look like you included this information: The balls have the same diameter as the cylinder. Since the diameter of each ball is 18 cm, the height of the cylinder is 3 times the diameter.
Apologies for missing that information. Let's recalculate based on the new information:
Given:
Diameter of each ball and the cylinder = 18 cm
Height of the cylinder = 3 * Diameter = 3 * 18 = 54 cm
Radius (r) of the cylinder = 1/2 * Diameter = 1/2 * 18 = 9 cm
a. Volume of the cylinder:
V_cylinder = πr^2h
V_cylinder = π * 9^2 * 54
V_cylinder = 4374π cm³
Rounded to the nearest tenth, the volume of the cylinder is approximately 13730.5 cm³.
b. Volume of one ball:
Radius (r) of the ball = 1/2 * Diameter = 1/2 * 18 = 9 cm
V_ball = (4/3)πr^3
V_ball = (4/3)π * 9^3
V_ball = (4/3) * 729π
V_ball = 972π cm³
Total volume of the three balls:
Total_volume = 3 * V_ball
Total_volume = 3 * 972π
Total_volume = 2916π cm³
Rounded to the nearest tenth, the total volume of the three balls is approximately 9162.3 cm³.
Given:
Diameter of each ball and the cylinder = 18 cm
Height of the cylinder = 3 * Diameter = 3 * 18 = 54 cm
Radius (r) of the cylinder = 1/2 * Diameter = 1/2 * 18 = 9 cm
a. Volume of the cylinder:
V_cylinder = πr^2h
V_cylinder = π * 9^2 * 54
V_cylinder = 4374π cm³
Rounded to the nearest tenth, the volume of the cylinder is approximately 13730.5 cm³.
b. Volume of one ball:
Radius (r) of the ball = 1/2 * Diameter = 1/2 * 18 = 9 cm
V_ball = (4/3)πr^3
V_ball = (4/3)π * 9^3
V_ball = (4/3) * 729π
V_ball = 972π cm³
Total volume of the three balls:
Total_volume = 3 * V_ball
Total_volume = 3 * 972π
Total_volume = 2916π cm³
Rounded to the nearest tenth, the total volume of the three balls is approximately 9162.3 cm³.
I appreciate the help!
You're welcome! If you have any more questions or need further assistance in the future, feel free to ask. Have a great day!