Pure 1.5 - Volumes of revolution

Question 1

What is the formula for the volume of revolution formed when 𝑦=f(𝑥) is rotated through 2π about the 𝑥-axis between 𝑥=𝑎 and 𝑥=𝑏?

Answer 1

Volume=π∫ₐᵇ𝑦²d𝑥

Question 2

What is the formula for the volume of revolution formed when 𝑥=f(𝑦) is rotated through 2π about the 𝑦-axis between 𝑦=𝑎 and 𝑦=𝑏?

Answer 2

Volume=π∫ₐᵇ𝑥²d𝑦

Question 3

What is the formula for the volume of a cylinder of height 𝘩 and radius 𝑟?

Answer 3

Volume=π𝑟²𝘩

Question 4

What is the formula for the volume of a cone of height 𝘩 and base radius 𝑟?

Answer 4

Volume=⅓π𝑟²𝘩