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Area and Volume Practice Tests

These Grade 10 Geometry practice tests develop measurement fluency with plane figures, surface area, volume, composite solids, scale factors, and real-world applications.

Skills covered

  • Calculating the area of rectangles, triangles, parallelograms, trapezoids, circles, rhombi, kites, and regular polygons
  • Finding surface area from faces, nets, and formulas for prisms, cylinders, pyramids, cones, spheres, and rectangular prisms
  • Finding volume of prisms, cylinders, pyramids, cones, spheres, cubes, and composite solids
  • Understanding square and cubic unit conversions and how area and volume scale
  • Applying area and volume to flooring, painting, packaging, aquariums, patios, tanks, and other practical measurements

How to use these practice tests

Sketch the figure, label the dimensions, and decide whether the problem asks for area, surface area, or volume. Keep square units for area and cubic units for volume.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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2. Test

Grade 10 Area and Volume Practice Tests

Practice Grade 10 Geometry questions about plane area, surface area, volume, prisms, cylinders, pyramids, cones, spheres, scale factors, and applications.

Choose the best answer. Identify the shape, select the correct formula, substitute the measurements, and report the answer with square or cubic units.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is the surface area of a rectangular prism?

Please select an answer first.

Correct answer: A

The correct answer is The sum of the areas of all six faces..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Surface area measures the total area covering a three-dimensional solid.
  3. Check the units: The correct answer is The sum of the areas of all six faces..

Surface area measures the total area covering a three-dimensional solid.

2. QuestionMultiple choice

What is the total surface area of a cylinder?

Please select an answer first.

Correct answer: B

The correct answer is 2πr2+2πrh2\pi r^2+2\pi rh..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A cylinder has two circular bases and a lateral rectangle, giving SA=2πr2+2πrhSA=2\pi r^2+2\pi rh.
  3. Check the units: The correct answer is 2πr2+2πrh2\pi r^2+2\pi rh..

A cylinder has two circular bases and a lateral rectangle, giving SA=2πr2+2πrhSA=2\pi r^2+2\pi rh.

3. QuestionMultiple choice

What is the surface area of a square pyramid?

Please select an answer first.

Correct answer: C

The correct answer is Base area plus the areas of its triangular lateral faces..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A pyramid’s surface area includes its base and every triangular lateral face.
  3. Check the units: The correct answer is Base area plus the areas of its triangular lateral faces..

A pyramid’s surface area includes its base and every triangular lateral face.

4. QuestionMultiple choice

What is the total surface area of a cone?

Please select an answer first.

Correct answer: D

The correct answer is πr2+πrℓ\pi r^2+\pi r\ell, where ℓ is slant height..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A cone has one circular base and a lateral area of πrℓ\pi r\ell.
  3. Check the units: The correct answer is πr2+πrℓ\pi r^2+\pi r\ell, where ℓ is slant height..

A cone has one circular base and a lateral area of πrℓ\pi r\ell.

5. QuestionMultiple choice

What is the surface area of a cube with side length s?

Please select an answer first.

Correct answer: A

The correct answer is 6s26s^2..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A cube has six congruent square faces, each with area s2s^2.
  3. Check the units: The correct answer is 6s26s^2..

A cube has six congruent square faces, each with area s2s^2.

6. QuestionMultiple choice

A rectangular prism has dimensions 2, 3, and 5. What is its surface area?

Please select an answer first.

Correct answer: B

The correct answer is 62 square units..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Use SA=2(lw+lh+wh)=2(6+10+15)=62SA=2(lw+lh+wh)=2(6+10+15)=62.
  3. Check the units: The correct answer is 62 square units..

Use SA=2(lw+lh+wh)=2(6+10+15)=62SA=2(lw+lh+wh)=2(6+10+15)=62.

7. QuestionMultiple choice

What does a net show for a three-dimensional solid?

Please select an answer first.

Correct answer: C

The correct answer is The two-dimensional faces arranged before folding..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A net is a flat pattern of the faces that folds into the solid.
  3. Check the units: The correct answer is The two-dimensional faces arranged before folding..

A net is a flat pattern of the faces that folds into the solid.

8. QuestionMultiple choice

What is the lateral surface area of a cylinder?

Please select an answer first.

Correct answer: D

The correct answer is 2πrh2\pi rh..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: Lateral area excludes the circular bases and measures the curved side: 2πrh2\pi rh.
  3. Check the units: The correct answer is 2πrh2\pi rh..

Lateral area excludes the circular bases and measures the curved side: 2πrh2\pi rh.

9. QuestionMultiple choice

What must be included when finding the surface area of a triangular prism?

Please select an answer first.

Correct answer: A

The correct answer is The two triangular bases and the three rectangular lateral faces..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: A triangular prism has two triangular bases and three rectangular lateral faces.
  3. Check the units: The correct answer is The two triangular bases and the three rectangular lateral faces..

A triangular prism has two triangular bases and three rectangular lateral faces.

10. QuestionMultiple choice

What is the surface area of a sphere with radius r?

Please select an answer first.

Correct answer: B

The correct answer is 4πr24\pi r^2..

  1. Identify the measurement model: Determine the base, height, radius, slant height, dimensions, or net shown in the problem.
  2. Apply the area or volume formula: The sphere surface area formula is SA=4πr2SA=4\pi r^2.
  3. Check the units: The correct answer is 4πr24\pi r^2..

The sphere surface area formula is SA=4πr2SA=4\pi r^2.

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