Washer Method Help Sheet
Vertical Rotation:


Change equation into the form x =
Use limits from the y-axis
Rotating the shape vertically from a line to the right of the curve.
The radius will be in the form:
Rotating the shape vertically from a line to the left of the
curve. The radius will be in the form:
𝑟𝑖 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑦 − 𝑎𝑥𝑖𝑠) − (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟𝑖 = (𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑥𝑖𝑠) + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑖𝑛𝑛𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟𝑜 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑦 − 𝑎𝑥𝑖𝑠) − (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟0 = (𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑥𝑖𝑠) + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
Horizontal Rotation:


Keep Equations in the form y =
Use limits from the x-axis
Rotating the shape horizontally from a line above the curve. The radius will
be in the form:
Rotating the shape horizontally from a line below the curve. The radius will
be in the form:
𝑟𝑖 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠) − (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟𝑖 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠) + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟𝑜 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠) − (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)
𝑟𝑜 = (𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑙𝑖𝑛𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠) + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑒𝑟 𝑐𝑢𝑟𝑣𝑒)