ATLAS Geometry Geometric Measurement and Dimension Practice

Geometric Measurement and Dimension skills

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone

Apply geometric concepts in modeling situations

Choose and produce an equivalent representation of a geometric theorem or formula

Standards basis

Arkansas Academic Standards for Mathematics (CCSS-M–aligned / Arkansas-adopted math standards) — Arkansas

How the ATLAS reports it

Arkansas’s statewide assessment system is ATLAS, which the ADE page says began serving in spring 2024. The official public page does not publish a math blueprint there, so the most defensible coverage map is the Arkansas math standards structure that ATLAS is aligned to.

Blueprint & weighting

ATLAS uses the Independent / state-specific framework (by grade domains structure).

Official sources

Arkansas DESE Assessment: Test Scores
Arkansas DESE home page
Arkansas DESE: 3–10 ATLAS Content Assessments

8 free questions · 0/0 correct

Practice playmedium

A storage tank holds liquid at a density of $8$ pounds per cubic foot. If the tank contains $1{,}920$ pounds of liquid, what is the volume of the liquid, in cubic feet?

Set up the proportion $\dfrac{8\text{ pounds}}{1\text{ cubic foot}} = \dfrac{1{,}920\text{ pounds}}{x\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $8x = 1{,}920\textsf{,}$ so $x = 240\text{ ft}^{3}\textsf{.}$

Practice playeasy

Find the volume of a cone with radius $2$ and height $6$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 4 \times 6 = 24$ .

Practice playmedium

A cylindrical rain barrel has an inside radius of $3$ feet. After a storm, the water level rises $4$ inches. What is the volume of the added water, in cubic feet?

Convert $4$ inches to $\dfrac{1}{3}$ foot. $V = \pi r^{2} h = \pi (3)^{2}\left(\dfrac{1}{3}\right) = 3\pi$ cubic feet.

Practice playmedium

A shipping crate has a volume of $160$ cubic feet and holds $4{,}800$ identical packages. What is the packaging density, in packages per cubic foot?

Set up the proportion $\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $160x = 4{,}800\textsf{,}$ so $x = 30\text{ packages per ft}^{3}\textsf{.}$

Practice playeasy

Find the volume of a cylinder with radius $2$ and height $5$ . Use $\pi = 3$ .

$V = \pi r^{2} h = 3 \times 4 \times 5 = 60$ .

Practice playhard

A concrete drainage pipe is a hollow right circular cylinder. The outer radius is $r_1 = 6$ meters, the inner radius is $r_2 = 4$ meters, and the pipe is $5$ meters long. What is the volume of concrete in the pipe wall, in cubic meters?

Wall volume is outer minus inner: $V = \pi h(r_1^{2} - r_2^{2}) = \pi (5)(6^{2} - 4^{2}) = \pi (5)(20) = 100\pi$ cubic meters.

Practice playmedium

A room heater uses energy at a density of $25$ BTUs per cubic foot. For a room with volume $120$ cubic feet, how many BTUs does the heater use?

Set up the proportion $\dfrac{25\text{ BTUs}}{1\text{ cubic foot}} = \dfrac{x\text{ BTUs}}{120\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $x = 25 \times 120 = 3{,}000\text{ BTUs}\textsf{.}$

Practice playeasy

A tent is a square pyramid with base side $6$ feet and height $4$ feet. Each camper needs $16$ cubic feet of air.

How many campers can the tent hold?