7th Grade Area, Volume and Surface Area Test with Point Values (PDF)

7th Grade math test: Area, Volume and Surface Area – Maths PDF

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This area volume surface area test for 7th Grade covers area, volume and surface area (Common Core 7.G.B.6), with a free PDF to print.

This 45-minute test checks the area of triangles, quadrilaterals, and polygons, and the volume and surface area of right prisms, including composite figures (Common Core 7.G.B.6). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Area, Volume and Surface Area
Standards: 7.G.B.6
Time: 45 minutes
Total: 20 points

Area volume surface area test: questions

Question 1 – Triangle [2 pts]

A triangle.

Find the area of the triangle.

Question 2 – Trapezoid [2 pts]

A trapezoid.

Find the area of the trapezoid.

Question 3 – Prism volume and surface [2 pts]

A rectangular prism.

Find the volume and the surface area of the prism.

Question 4 – Triangular prism [2 pts]

A triangular prism has a right triangle base with legs of 6 in and 8 in. The prism is 9 in long. Find its volume.

Question 5 – Composite figure [2 pts]

A figure is a 12-ft by 9-ft rectangle with a 3-ft by 4-ft rectangle cut out of one corner. Find its area.

Question 6 – Missing height [2 pts]

A rectangular prism has a base of 6 cm by 5 cm and a volume of 150 cubic centimeters. Find its height and surface area.

Question 7 – Pool water [2 pts]

A pool is 25 ft by 10 ft and 4 ft deep. Find the volume of water when the pool is filled to a depth of 3 ft. Then find the percent of the pool’s volume that is filled.

Question 8 – Net [3 pts]

A net of a box.

Name the solid and give its dimensions. (1 point)
Find the surface area using the net. (1 point)
Find the volume. (1 point)

Question 9 – Wedge of cheese [3 pts]

A wedge of cheese.

Find the area of the triangular end. (1 point)
Find the volume of the cheese. (1 point)
Cheese costs $0.05 per cubic inch. Find the cost of the wedge. (1 point)

Key facts behind this area volume surface area test

Key facts

Triangle: $A = \frac{1}{2} bh$. Trapezoid: $A = \frac{1}{2} (b_1 + b_2) h$.
Composite polygon: add the areas of simple pieces or subtract a missing piece.
Volume of a prism: $V = Bh$ (base area times height).
Surface area of a prism: add the areas of all faces from the net.
Area uses square units; volume uses cubic units.

How to use this area volume surface area test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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