Area/volume

Question 1

Formula for area

Answer 1

$(upper-lower)

Question 2

Find volume rotating about

Answer 2

€$(upper-lower)^2 disk

€$(upper)^2-(lower)^2 washer

Question 3

Volume rotated about y=a (a above area)

Answer 3

V= €$(a-furthest)^2-(a-closest)^2 dx

Question 4

Volume rotated about y=a (a below area)

Answer 4

V= €$(a+furthest)^2-(a+closest)^2 dx

Question 5

Volume rotated about y=a (a left of area)

Answer 5

V= €$(a+furthest)^2-(a+closest)^2 dy

Question 6

Volume rotated about y=a (a right of area)

Answer 6

V= €$(a-furthest)^2-(a-closest)^2 dy

Question 7

Cross sections- square

Answer 7

$(side)^2 side=(upper-lower)

Question 8

Cross sections- equilateral triangle

Answer 8

(Sqrt(3)/4) $(side)^2 side=(upper-lower)

Question 9

Cross sections- isosceles triangle

Answer 9

(1/4) $(side)^2 side=(upper-lower)

Question 10

Cross sections- right triangle

Answer 10

(1/2) $(side)^2 side=(upper-lower)

Question 11

Cross sections- semi circle

Answer 11

(€/8) $(side)^2 side=(upper-lower)

Question 12

Arc length (rectangular)

Answer 12

$(sqrt(1+(f’x)^2))