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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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3. 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 volume of a prism?

Please select an answer first.

Correct answer: A

The correct answer is V=BhV=Bh, where B is base area..

  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 prism’s volume is base area multiplied by perpendicular height.
  3. Check the units: The correct answer is V=BhV=Bh, where B is base area..

A prism’s volume is base area multiplied by perpendicular height.

2. QuestionMultiple choice

What is the volume of a cylinder?

Please select an answer first.

Correct answer: B

The correct answer is V=πr2hV=\pi r^2h..

  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 is a circular prism, so its volume is V=πr2hV=\pi r^2h.
  3. Check the units: The correct answer is V=πr2hV=\pi r^2h..

A cylinder is a circular prism, so its volume is V=πr2hV=\pi r^2h.

3. QuestionMultiple choice

What is the volume of a pyramid?

Please select an answer first.

Correct answer: C

The correct answer is V=13BhV=\frac{1}{3}Bh..

  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 has one-third the volume of a prism with the same base area and height.
  3. Check the units: The correct answer is V=13BhV=\frac{1}{3}Bh..

A pyramid has one-third the volume of a prism with the same base area and height.

4. QuestionMultiple choice

What is the volume of a cone?

Please select an answer first.

Correct answer: D

The correct answer is V=13πr2hV=\frac{1}{3}\pi r^2h..

  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-third the volume of a cylinder with the same radius and height.
  3. Check the units: The correct answer is V=13πr2hV=\frac{1}{3}\pi r^2h..

A cone has one-third the volume of a cylinder with the same radius and height.

5. QuestionMultiple choice

What is the volume of a sphere?

Please select an answer first.

Correct answer: A

The correct answer is V=43πr3V=\frac{4}{3}\pi r^3..

  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 volume formula is V=43πr3V=\frac{4}{3}\pi r^3.
  3. Check the units: The correct answer is V=43πr3V=\frac{4}{3}\pi r^3..

The sphere volume formula is V=43πr3V=\frac{4}{3}\pi r^3.

6. QuestionMultiple choice

What is the volume of a rectangular prism with dimensions 3, 4, and 6?

Please select an answer first.

Correct answer: B

The correct answer is 72 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: Multiply the dimensions: V = 3 · 4 · 6 = 72 cubic units.
  3. Check the units: The correct answer is 72 cubic units..

Multiply the dimensions: V = 3 · 4 · 6 = 72 cubic units.

7. QuestionMultiple choice

What is the volume of a cube with side length 5?

Please select an answer first.

Correct answer: C

The correct answer is 125 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: A cube’s volume is s3=53=125s^3=5^3=125.
  3. Check the units: The correct answer is 125 cubic units..

A cube’s volume is s3=53=125s^3=5^3=125.

8. QuestionMultiple choice

A solid is made of two nonoverlapping prisms. How can its volume be found?

Please select an answer first.

Correct answer: D

The correct answer is Add the volumes of the two prisms..

  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 volume of a composite solid is the sum of the volumes of its nonoverlapping parts.
  3. Check the units: The correct answer is Add the volumes of the two prisms..

The volume of a composite solid is the sum of the volumes of its nonoverlapping parts.

9. QuestionMultiple choice

What are the units for volume?

Please select an answer first.

Correct answer: A

The correct answer is 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: Volume measures three-dimensional space, so its units are cubic.
  3. Check the units: The correct answer is Cubic units..

Volume measures three-dimensional space, so its units are cubic.

10. QuestionMultiple choice

If all lengths of a solid are multiplied by 3, how does its volume change?

Please select an answer first.

Correct answer: B

The correct answer is It is multiplied by 27..

  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: Volume scales by the cube of the length factor: 33=273^3=27.
  3. Check the units: The correct answer is It is multiplied by 27..

Volume scales by the cube of the length factor: 33=273^3=27.

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