2024 HSC Mathematics Extension 1
Question 12(b):
Volume of revolution
The region is bounded by the function , the -axis and the lines and .
What is the volume of the solid of revolution obtained when the region is rotated 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
- Disk method: .
- Primitive: .
- NESA 12(b): 3 marks correct; 2 marks for the correct primitive; 1 mark for a correct volume integral expression.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 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
Find the volume generated when from to is rotated about the -axis.
Question 2
Find the volume when from to is rotated about the -axis.
Question 3
Write an integral for the volume of on about the -axis, then evaluate it exactly.