Multi-step perimeter, area, and volume (ACT). Game on.

Multi-step perimeter, area, and volume (ACT) is a grade 7 math skill aligned to Common Core standard 7.G.B.6: solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects. Below are 3 practice questions with answers and step-by-step explanations, drawn from the 7 multi-step perimeter, area, and volume (act) problems our math games drill.

CCSS 7.G.B.67 questions in the bank

Kickoff

3 plays. No signup.

Warm-uphard

A rectangular prism has volume $72$ cubic centimeters and height $4$ centimeters. The length is twice the width. What is the width, in centimeters?

$V = \ell w h$ and $\ell = 2w$ , so $72 = (2w)(w)(4) = 8w^2$ . Then $w^2 = 9$ and $w = 3\text{ cm}\textsf{.}$

Mid-gamehard

A rectangular prism has volume $160$ cubic inches and height $5$ inches. The length is twice the width. What is the length, in inches?

$V = \ell w h$ and $\ell = 2w$ , so $160 = (2w)(w)(5) = 10w^2$ . Then $w^2 = 16$ , so $w = 4$ and $\ell = 8\text{ in}\textsf{.}$

Buzzer beaterhard

A rectangular prism has a square base and height $6$ meters. Its volume is $96$ cubic meters. What is the side length of the base, in meters?

$V = s^2 h$ , so $96 = s^2 \cdot 6$ and $s^2 = 16$ . Then $s = 4\text{ m}\textsf{.}$

Overtime

4 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover multi-step perimeter, area, and volume (act):

NAEP SBAC SAT SC READY NC EOG/EOC

Reporting domains for this skill

SAT All grades: Geometry and Trigonometry ACT All grades: Preparing for Higher Math STAAR Grade 7: Geometry and Measurement STAAR Grade 8: Geometry and Measurement MAP Growth Math 6+: Geometry i-Ready Grade 7: Geometry

More Grade 7 skills

Probability basics Simple interest One-event probability word problems Probability from number sets Ratios, rates, and proportions Surface area in context (SAT)Table problems with percents and ratios (ACT)Three integers in a given ratio (ACT)All Grade 7 practice →

Drill it inside a game.

The free placement test finds your level, then every match serves multi-step perimeter, area, and volume (act) questions at exactly the right difficulty.