Year 9 - Surface area and volume - Free practice
Year 9 Surface Area & Volume Worksheets
Cylinders, prisms, composite 3D objects.
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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
Textbook questions won't lift a test mark.
They come sorted by topic, so your child knows the method before they read the question.
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About this worksheet
Why we built it
Year 9 takes 3D measurement up a level - cylinders, composite prisms, and surface area for the first time. These worksheets give your student varied 3D objects so they get comfortable identifying which formula applies to which face.
What's covered
Sub-skills your student will practise
- ✓Surface area of right prisms (rectangular, triangular)
- ✓Surface area of cylinders (curved + two circles)
- ✓Volume of cylinders
- ✓Composite solids (prism + prism, prism + cylinder)
- ✓Real-world problems (paint, packaging, capacity)
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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
Rebecca M.
Year 8 · Maths
“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”
Priya S.
Year 9 · Maths
“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”
Ella, student
Year 10 · Maths
Frequently asked
Questions parents ask about surface area and volume
What's the surface area of a cylinder?
Two circles (top and bottom) plus the curved side, which unrolls into a rectangle. So SA = 2 x pi x r^2 + 2 x pi x r x h. The 2 x pi x r is the circumference, which becomes the width of the unrolled rectangle.
How is Year 9 SA harder than Year 8?
Year 9 includes cylinders (curved surfaces) and composite solids (a cylinder on top of a rectangular prism, say). Students have to think about which faces are hidden inside the join and not counted.
What's the volume formula for a cylinder?
V = pi x r^2 x h - the area of the circular base times the height. Same pattern as a prism: cross-section area times length.
How do students approach a composite solid?
Split it into individual shapes, calculate the volume or SA of each, then add (for volume) or subtract any hidden faces (for SA). The hidden-face check is what catches Year 9 students out.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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Talk to us about Year 9 surface area and volume.
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