Grade 9 Geometry & Measurement Worksheets
Free printable geometry & measurement practice for Grade 9 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 9 Geometry & Measurement Practice
Solve each problem. Show your work.
- 1.A closed cylinder has radius 3 cm and height 7 cm. Find its total surface area in terms of π: _____
- 2.A rectangular prism has volume 224 cm³, length 8 cm, and width 7 cm. Find its height: _____
- 3.An L-shape is a 10 cm by 8 cm rectangle with a 4 cm by 3 cm corner removed. Find its area: _____
- 4.A closed cylinder has radius 6 cm and height 5 cm. Find its total surface area in terms of π: _____
- 5.A rectangular prism has volume 200 cm³, length 10 cm, and width 5 cm. Find its height: _____
- 6.An L-shape is a 12 cm by 8 cm rectangle with a 4 cm by 3 cm corner removed. Find its area: _____
Show answer key
- Question 1: 60π cm²
- Question 2: 4 cm
- Question 3: 68 cm²
- Question 4: 132π cm²
- Question 5: 4 cm
- Question 6: 84 cm²
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Calculate the circumference of a circle with a radius of 7 cm. (Use pi = 3.14)
- 2.Calculate the area of a circle with a radius of 10 cm. (Use pi = 3.14)
- 3.Find the volume of a rectangular prism with length 5 cm, width 4 cm, and height 3 cm.
- 4.A composite shape is made of a cube with a side length of 2 cm sitting on top of another cube with a side length of 4 cm. Calculate the total volume.
- 5.Two parallel lines are intersected by a transversal. If one interior angle is 70 degrees, what is the measure of its corresponding angle?
- 6.Find the sum of the interior angles of a pentagon using the formula (n-2) * 180, where n is the number of sides.
A selection of topic skills
Solve each problem. Show your work.
- 1.A circle has a diameter of 14 cm. Calculate the circumference and the area of the circle. Use 3.14 for pi. Round your answers to the nearest hundredth.
- 2.A composite 3D object is made of a rectangular prism with dimensions 5 cm by 4 cm by 10 cm and a cube with a side length of 3 cm attached to the top. Calculate the total volume of this composite object.
- 3.Two parallel lines are intersected by a transversal. If one interior angle is 65 degrees, find the measures of the other seven angles formed by the transversal.
- 4.A cylindrical water tank has a radius of 2 meters and a height of 5 meters. If the tank is currently 3/4 full, how many cubic meters of water are in the tank? (Use 3.14 for pi)
- 5.Determine the sum of the interior angles of a convex polygon with 9 sides. Then, find the measure of one interior angle if the polygon is a regular polygon.
- 6.You are painting a storage shed that is a rectangular prism 8 feet long, 6 feet wide, and 7 feet high. If you do not paint the floor or the roof, what is the total surface area you need to paint?
What Your Child Will Learn
Grade 9 geometry and measurement extends what students learned about area and volume in elementary school to more complex and composite shapes, while introducing circle geometry properties for the first time. Students calculate the circumference and area of circles, and then apply those formulas within composite figures — shapes built from combinations of rectangles, triangles, circles, and semicircles.
The measurement side of the unit covers surface area and volume of 3D solids including cylinders, cones, spheres, and composite solids, often in applied contexts like packaging, construction, or capacity problems. Students also work with optimization-style questions, such as finding the dimensions that minimize surface area for a given volume, which previews the optimization thinking used in later calculus.
Precision with formulas and units is emphasized throughout — students must select the correct formula, substitute values carefully, and keep units consistent (especially when converting between measurement units or working with derived units like cm² and cm³). This attention to formula selection and unit tracking is a skill that carries directly into trigonometry the following year.
Skills Covered
- Calculating circumference and area of circles
- Finding area and perimeter of composite 2D shapes
- Calculating surface area of cylinders, cones, and spheres
- Calculating volume of prisms, cylinders, cones, and spheres
- Solving composite-solid problems combining multiple formulas
- Applying optimization reasoning to measurement problems
Curriculum Aligned: Part of the de-streamed Grade 9 math course (MTH1W in Ontario), covering the geometry and measurement strand, including circle properties and 3D surface area/volume.
Parent Tip: Formula sheets are normal and expected at this level, so don't worry if you don't have the surface-area formulas memorized yourself. What helps most is asking your teen which formula they chose for a problem and why — catching a mismatched formula (using a cylinder formula for a cone, for instance) is something you can spot together without doing the math.
What your child will practice
- Geometric PropertiesApply geometric properties and relationships to solve problems involving angles, parallel lines, and polygons.
- Circle PropertiesInvestigate and apply relationships involving the circle, including circumference, area, and central angles.
- Surface Area and VolumeSolve problems involving the surface area and volume of composite 3D objects.
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Check my workFrequently Asked Questions
How often should my child practice geometry & measurement?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.