2025 HSC Mathematics Extension 1
Question 12(b):
Volume of revolution
Rotate the region between , the -axis, and about the -axis.
How to recognise this question
Question type: volumes of revolution
- The command and notation point to volumes of revolution.
- The requested response is a worked solution.
How to handle it: identify the radius and use the disk or washer formula with the correct variable and bounds.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Since , the disk radius at height y is .
- .
- .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Rotate the region , about the y-axis. Find the volume.
Question 2
Rotate the region between and , , about the x-axis.
Question 3
Rotate the region under , , about the x-axis.