NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

5. 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

A rectangular floor is 12 ft by 15 ft. What area must be covered with flooring?

Please select an answer first.

Correct answer: A

The correct answer is 180 square feet..

  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 length and width: 12 · 15 = 180 square feet.
  3. Check the units: The correct answer is 180 square feet..

Multiply length and width: 12 · 15 = 180 square feet.

2. QuestionMultiple choice

An aquarium measures 20 in by 10 in by 12 in. What is its capacity?

Please select an answer first.

Correct answer: B

The correct answer is 2,400 cubic inches..

  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 rectangular-prism volume is 20 · 10 · 12 = 2,400 cubic inches.
  3. Check the units: The correct answer is 2,400 cubic inches..

The rectangular-prism volume is 20 · 10 · 12 = 2,400 cubic inches.

3. QuestionMultiple choice

A room has four walls, each 10 ft by 8 ft. Ignoring doors and windows, what wall area will be painted?

Please select an answer first.

Correct answer: C

The correct answer is 320 square feet..

  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: Each wall is 80 square feet; four walls require 4 · 80 = 320 square feet.
  3. Check the units: The correct answer is 320 square feet..

Each wall is 80 square feet; four walls require 4 · 80 = 320 square feet.

4. QuestionMultiple choice

Why is a net useful when designing a box?

Please select an answer first.

Correct answer: D

The correct answer is It shows the flat faces needed to calculate material and surface 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 net displays every face, making surface-area and material calculations possible.
  3. Check the units: The correct answer is It shows the flat faces needed to calculate material and surface area..

A net displays every face, making surface-area and material calculations possible.

5. QuestionMultiple choice

Two similar solids have length scale factor 2. What is the surface-area scale factor?

Please select an answer first.

Correct answer: A

The correct answer is 4..

  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 scales by the square of the length factor: 22=42^2=4.
  3. Check the units: The correct answer is 4..

Surface area scales by the square of the length factor: 22=42^2=4.

6. QuestionMultiple choice

Two similar solids have length scale factor 2. What is the volume scale factor?

Please select an answer first.

Correct answer: B

The correct answer is 8..

  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: 23=82^3=8.
  3. Check the units: The correct answer is 8..

Volume scales by the cube of the length factor: 23=82^3=8.

7. QuestionMultiple choice

A circular patio has radius 6 m. What area of tile is needed?

Please select an answer first.

Correct answer: C

The correct answer is 36π36\pi square meters..

  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 patio area is A=π(6)2=36πA=\pi(6)^2=36\pi square meters.
  3. Check the units: The correct answer is 36π36\pi square meters..

The patio area is A=π(6)2=36πA=\pi(6)^2=36\pi square meters.

8. QuestionMultiple choice

A cylindrical water tank has radius 2 m and height 10 m. What is its volume?

Please select an answer first.

Correct answer: D

The correct answer is 40π40\pi cubic meters..

  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(2)2(10)=40πV=\pi r^2h=\pi(2)^2(10)=40\pi.
  3. Check the units: The correct answer is 40π40\pi cubic meters..

Use V=πr2h=π(2)2(10)=40πV=\pi r^2h=\pi(2)^2(10)=40\pi.

9. QuestionMultiple choice

What shape is formed by a cross-section parallel to the base of a rectangular prism?

Please select an answer first.

Correct answer: A

The correct answer is A rectangle..

  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 plane parallel to a rectangular prism’s base creates a congruent rectangular cross-section.
  3. Check the units: The correct answer is A rectangle..

A plane parallel to a rectangular prism’s base creates a congruent rectangular cross-section.

10. QuestionMultiple choice

Which formula should be used for the volume of a cone?

Please select an answer first.

Correct answer: B

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 is one-third 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 is one-third of a cylinder with the same radius and height.

Previous testNext test