#shell method

does anyone knows how to find the radius of the revolution of a solid using Shell method? But not as in x-axis or y-axis, but it'd be about y=-1, x=4,x=-3.

If you’ve taken calculus, you’ll no doubt recall the “shell method” for finding the volume of a rotated object, such as a torus (a fried 3D object parameterized using equations defined by Krispy Kreme). The method works by adding up infinitesimally thin shells, from the inside to the outside. Think of blasting off of Saturn and passing through the widening rings.  

  Making a similar voyage in Bible studies can reveal some fascinating patterns often only uncovered by theologians. It helps to be curious. Given a topic or person, you can begin by looking at the same or related things a little bit further out in expanding rings of focus – a chapter, a book, or maybe a couple books away. What happened to this person as time went on? Where have I seen this name or idea before?

If you ping the Bible with a broad search and see the relationships change and maturate, you can gain some rare insight. It happens when we encounter two paired ideas - similar, but slightly different - striking out an octave on the keys of our understanding.

  Here are some examples as applied to biblical, non-toroidal objects:

Passage A: “Follow me, and I will make you fishers of men.” – Matthew 4:19 Passage B: “If I want him to remain alive until I return, what is that to you? You must follow me.” – John 21:22 Finding: “Follow me” was Jesus’ command to Peter from the very beginning; with these words, he first called Peter, and with these words, he commissioned him to become the rock of the church.

  Passage A: “He got up, rebuked the wind, and said to the waves, “Quiet! Be still!” Then the wind died down and it was completely calm.” - Mark 4:39 Passage B: “When they came to Jesus, they saw the man who had been possessed by the legion of demons, sitting there, dressed and in his right mind; and they were afraid.” – Mark 5:15 Finding: Jesus calmed the man just as he had calmed the sea a few hours before.

  Passage A: “The virgin will conceive and give birth to a son, and they will call him Immanuel (which means “God with us”).” – Matthew 1:23 Passage B: “… And surely I am with you always, to the very end of the age.” – Matthew 28:20 Finding: Matthew both begins and ends with Immanuel (God with us).

  Passage A: “For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God.” - 1 Corinthians 15:9 Passage B: “Although I am less than the least of all the Lord’s people, this grace was given me: to preach to the Gentiles the boundless riches of Christ…” – Ephesians 3:8 Passage C: “Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners—of whom I am the worst.” – 1 Timothy 1:15 Finding: As Paul’s life went on, he realized more and more how inadequate he was before God. Paul shows a progression of humility (i.e. from “least of apostles” to “chief of sinners” from Corinthians to Timothy).

  Passage A: “God is spirit, and his worshipers must worship in the Spirit and in truth.” - John 4:24 Passage B: “…God is light; in him there is no darkness at all.” – 1 John 1:5 Passage C: “Whoever does not love does not know God, because God is love.” – 1 John 4:8 Finding: John reveals three key themes of God's nature in his letters – God is Spirit, God is light, and God is love.

Narrowing your focus, you might be able to even apply the method within the same story:

Passage A: "Martha answered, “I know he will rise again in the resurrection at the last day.” Jesus said to her, “I am the resurrection and the life. The one who believes in me will live, even though they die…”" – John 11:24 Passage B: "When Mary reached the place where Jesus was and saw him, she fell at his feet and said, “Lord, if you had been here, my brother would not have died.” When Jesus saw her weeping, and the Jews who had come along with her also weeping, he was deeply moved in spirit and troubled…Jesus wept." – John 11:32 Finding: Martha revealed Christ’s deity as He spoke of Himself, and Mary uncovered Christ’s humanity as He wept.

Passage A1: When a Samaritan woman came to draw water, Jesus said to her, “Will you give me a drink?” – John 4:7 Passage B1: Meanwhile his disciples urged him, “Rabbi, eat something.” But he said to them, “I have food to eat that you know nothing about.” Then his disciples said to each other, “Could someone have brought him food?” “My food,” said Jesus, “is to do the will of him who sent me and to finish his work. – John 4:34 Passage A2: “Go, call your husband and come back.” “I have no husband,” she replied. – John 4:16-17 Passage B2: Then, leaving her water jar, the woman went back to the town and said to the people, “Come, see a man who told me everything I ever did. Could this be the Messiah?” They came out of the town and made their way toward him. – John 4:28 Finding: The Samaritan woman inadvertently fulfilled every single request Jesus made of her. By believing in Jesus, she responded to his first request, allowing Jesus to save her and do the will of the Father; by bringing her entire town to Christ, she answered the second.

Applying this technique for Bible passages makes some very high-level strokes stand out on the canvas of the Bible – things conceived by God to marvel at. I still have great difficulty in finding and linking concepts from across “far distances.” It’s likely due to my need of a firmer grasp on scripture. But it’s a diamond mine for theologians, I would guess. Fortunately, no license is required to start digging.

like

we never did shells

and now i'm college

and i'm just like

Like about finding the volume of a solid revolved around an axis or whatever?

y=2- (1/2)x , y=0, x=1, x=2,rotated about the x-axis.

Or if you could, a general explanation of how I could use the shell method in any situation. I want to know, because I know I can use the shell method for ALL rotational solids.