Someone please help,I have to sleep just 2 questions idk how to do
6. The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.
(Since I can't post picture here)
The diagram: ◒
a) If the maximum depth of the water is 2cm and the radius of the pope is 7cm, find the area shaded.
b)What is the volume of water in a pipe length of 30cm?
An equilateral triangle is inscribed in a circle of radius 18.8cm.
the diagram: ⎊
Find:
a)area of the triangle
b)area of the three segments surrounding the triangle.
The area of a segment subtended by an angle θ is
1/2 r^2 (θ - sinθ)
So, what is θ ?
If you draw the diagram, you can see that cos(θ/2) = 5/7
Now, the volume of water is the area of the segment times the length
(b) The side of an equilateral triangle inscribed in a circle of radius r is
s = r√3
And, yu know the area of an equilateral triangle of side s is
a = √3/4 s^2 = √3/4 (3r^2)
And of course, the 3 segments outside the triangle are just the area of the circle less that of the triangle.
So just plug and chug.
And no, I did not know these handy formulas off the top of my head. But it only took me about a minute with google. Try it some time.
find angle center theta = 2 cos^-1 ( 5/7 ) = 2 cos^-1 .7143 = 88.8 degrees
A of segment = (1/2)R^2 (theta - sin theta) = (49/2) (theta in radians - sin theta) = 49/2 ( 1.55-1)
= 13.47 cm^2
times 30 = 404 cm^3
a) To find the area of the shaded region in the cylindrical pipe, we need to find the area of the water surface that is exposed. Since the water is lying in the bottom, it forms a circular shape with a radius of 7cm.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. Therefore, the area of the water surface is A = π(7cm)^2.
Using the value of pi as 3.14, we can calculate the area as follows:
A = 3.14 * (7cm)^2
A = 3.14 * 49cm^2
A ≈ 153.86cm^2
Thus, the area of the shaded region is approximately 153.86 square centimeters.
b) To find the volume of water in a pipe of length 30cm, we need to calculate the volume of a cylinder.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
In this case, the radius of the pipe is 7cm and the height or length of the pipe is 30cm. Therefore, substituting these values into the formula, we get:
V = 3.14 * (7cm)^2 * 30cm
V ≈ 4617.6cm^3
Hence, the volume of water in a pipe with a length of 30cm is approximately 4617.6 cubic centimeters.
Moving on to the second problem:
a) An equilateral triangle is inscribed in a circle of radius 18.8cm. To find the area of the triangle, we can use the formula A = (s^2 * sqrt(3))/4, where A is the area and s is the side length of the triangle.
Since it is an equilateral triangle, the radius of the circle is also the same as the side length of the triangle. Therefore, the area of the triangle is:
A = (18.8cm)^2 * sqrt(3)/4
A ≈ 155.06cm^2
Thus, the area of the equilateral triangle is approximately 155.06 square centimeters.
b) To find the area of the three segments surrounding the triangle, we need to subtract the area of the triangle from the area of the circle.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. Substituting the radius of 18.8cm, we have:
A_circle = π * (18.8cm)^2
The total area covered by the three segments is the area of the circle minus the area of the triangle:
A_segments = A_circle - A_triangle
Using the value of pi as 3.14, we can calculate the area as follows:
A_segments = 3.14 * (18.8cm)^2 - 155.06cm^2
Hence, the area of the three segments surrounding the triangle is approximately (3.14 * (18.8cm)^2) - 155.06cm^2.
I can help you with these questions. Let's break them down one by one.
For the first question:
a) To find the area shaded, we need to calculate the area of the circular base and subtract the area of the water surface.
The area of the circular base is given by the formula A = π * r^2, where A is the area and r is the radius of the cylinder. In this case, the radius is 7cm. So the area of the circular base is A = π * 7^2 square cm.
To find the area of the water surface, we need to calculate the area of the circle with a radius of 7cm (since this is the maximum depth of the water). Therefore, the area of the water surface is also A = π * 7^2 square cm.
Finally, to find the shaded area, we subtract the area of the water surface from the area of the circular base: Shaded Area = (π * 7^2) - (π * 7^2) square cm = 0 square cm.
Therefore, the shaded area is 0 square cm.
b) To find the volume of water in a pipe length of 30cm, we need to calculate the volume of the cylindrical pipe.
The volume of a cylinder is given by the formula V = A * h, where V is the volume, A is the base area, and h is the height of the cylinder. In this case, the height of the cylinder is 30cm.
The base area of the cylinder is the same as the area of the circular base, which we calculated earlier as A = π * 7^2 square cm.
Thus, the volume of water in the pipe is V = (π * 7^2) * 30 cubic cm.
You can now solve for the numerical value by substituting the value of π (approximately 3.14159) and calculate the final answer.
Moving on to the second question:
a) To find the area of the inscribed equilateral triangle, we need to calculate the side length of the triangle first.
In an equilateral triangle, all sides are equal. The side length of the triangle can be found using the formula s = 2r, where s is the side length and r is the radius of the circumscribed circle. In this case, the radius is given as 18.8cm.
So, the side length of the triangle is s = 2 * 18.8 cm.
To find the area of an equilateral triangle, we use the formula A = (sqrt(3)/4) * s^2, where A is the area and s is the side length.
Therefore, the area of the equilateral triangle is A = (sqrt(3)/4) * (2 * 18.8)^2 square cm.
b) To find the area of the three segments surrounding the triangle, we need to calculate the area of the three sectors and subtract the area of the triangle.
Each sector is formed by two radii and their corresponding arc. The angle of each sector can be found using the formula θ = 360° / 3 (since there are three sectors in a circle). In this case, θ = 120°.
The area of each sector is given by the formula A_sector = (θ/360) * π * r^2, where A_sector is the area of the sector and r is the radius of the circle.
Thus, the area of the three sectors is A_sectors = 3 * (θ/360) * π * r^2 square cm.
To find the area of the three segments surrounding the triangle, we subtract the area of the triangle from the area of the three sectors: Area of segments = A_sectors - A_triangle.
You can calculate the numerical values by substituting the known values of θ, π, and r.
I hope this helps! Feel free to ask if you have any further questions.