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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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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 volume of a cylinder with radius 3 and height 5?

Please select an answer first.

Correct answer: A

The correct answer is 45π45\pi cubic 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 V=πr2h=π(3)2(5)=45πV=\pi r^2h=\pi(3)^2(5)=45\pi.
  3. Check the units: The correct answer is 45π45\pi cubic units..

Use V=πr2h=π(3)2(5)=45πV=\pi r^2h=\pi(3)^2(5)=45\pi.

2. QuestionMultiple choice

What is the volume of a cone with radius 3 and height 4?

Please select an answer first.

Correct answer: B

The correct answer is 12π12\pi cubic 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 V=13π(3)2(4)=12πV=\frac{1}{3}\pi(3)^2(4)=12\pi.
  3. Check the units: The correct answer is 12π12\pi cubic units..

Use V=13π(3)2(4)=12πV=\frac{1}{3}\pi(3)^2(4)=12\pi.

3. QuestionMultiple choice

What is the volume of a sphere with radius 3?

Please select an answer first.

Correct answer: C

The correct answer is 36π36\pi cubic 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 V=43π(3)3=36πV=\frac{4}{3}\pi(3)^3=36\pi.
  3. Check the units: The correct answer is 36π36\pi cubic units..

Use V=43π(3)3=36πV=\frac{4}{3}\pi(3)^3=36\pi.

4. QuestionMultiple choice

A prism has base area 24 and height 7. What is its volume?

Please select an answer first.

Correct answer: D

The correct answer is 168 cubic 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 V = Bh = 24 · 7 = 168 cubic units.
  3. Check the units: The correct answer is 168 cubic units..

Use V = Bh = 24 · 7 = 168 cubic units.

5. QuestionMultiple choice

A pyramid has base area 30 and height 9. What is its volume?

Please select an answer first.

Correct answer: A

The correct answer is 90 cubic 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 V=13Bh=13(30)(9)=90V=\frac{1}{3}Bh=\frac{1}{3}(30)(9)=90.
  3. Check the units: The correct answer is 90 cubic units..

Use V=13Bh=13(30)(9)=90V=\frac{1}{3}Bh=\frac{1}{3}(30)(9)=90.

6. QuestionMultiple choice

What is the surface area of a cube with side length 4?

Please select an answer first.

Correct answer: B

The correct answer is 96 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=6s2=6(42)=96SA=6s^2=6(4^2)=96.
  3. Check the units: The correct answer is 96 square units..

Use SA=6s2=6(42)=96SA=6s^2=6(4^2)=96.

7. QuestionMultiple choice

What is the total surface area of a cylinder with r = 2 and h = 5?

Please select an answer first.

Correct answer: C

The correct answer is 28π28\pi 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=2πr2+2πrh=8π+20π=28πSA=2\pi r^2+2\pi rh=8\pi+20\pi=28\pi.
  3. Check the units: The correct answer is 28π28\pi square units..

Use SA=2πr2+2πrh=8π+20π=28πSA=2\pi r^2+2\pi rh=8\pi+20\pi=28\pi.

8. QuestionMultiple choice

A cone has radius 5 and slant height 13. What is its lateral surface area?

Please select an answer first.

Correct answer: D

The correct answer is 65π65\pi 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: Lateral cone area is πrℓ=π(5)(13)=65π\pi r\ell=\pi(5)(13)=65\pi.
  3. Check the units: The correct answer is 65π65\pi square units..

Lateral cone area is πrℓ=π(5)(13)=65π\pi r\ell=\pi(5)(13)=65\pi.

9. QuestionMultiple choice

What is the surface area of a rectangular prism with dimensions 3, 4, and 5?

Please select an answer first.

Correct answer: A

The correct answer is 94 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(3⋅4+3⋅5+4⋅5)=2(47)=94SA=2(3\cdot4+3\cdot5+4\cdot5)=2(47)=94.
  3. Check the units: The correct answer is 94 square units..

Use SA=2(3⋅4+3⋅5+4⋅5)=2(47)=94SA=2(3\cdot4+3\cdot5+4\cdot5)=2(47)=94.

10. QuestionMultiple choice

How many cubic centimeters are in 0.003 cubic meters?

Please select an answer first.

Correct answer: B

The correct answer is 3,000 cm³..

  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: Because 1 m³ = 1,000,000 cm³, 0.003 m³ = 3,000 cm³.
  3. Check the units: The correct answer is 3,000 cm³..

Because 1 m³ = 1,000,000 cm³, 0.003 m³ = 3,000 cm³.

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