DC CAPE Geometry Geometric Measurement and Dimension Practice

Geometric Measurement and Dimension skills

explain volume formulas and use them to solve problems

visualize relationships between two-dimensional and three-dimensional objects

apply geometric concepts in modeling situations

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

8 free questions · 0/0 correct

Practice playmedium

A metal sample has a mass of $540$ kilograms and a density of $12$ kilograms per cubic meter. What is the volume of the sample, in cubic meters?

Set up the proportion $\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.}$ Cross-multiplying gives $12x = 540\textsf{,}$ so $x = 45\text{ m}^{3}\textsf{.}$

Practice playeasy

Find the volume of a cylinder with radius $2$ and height $4$ . Use $\pi = 3$ .

$V = \pi r^2 h = 3 \times 4 \times 4 = 48$ .

Practice playeasy

A culvert pipe is a right circular cylinder with an inside diameter of $12$ inches and a length of $20$ inches. What is the volume of the pipe's interior, in cubic inches?

The radius is $6$ inches. $V = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi$ cubic inches.

Practice playeasy

Riverside has a population density of $1{,}250$ people per square mile and an area of $48$ square miles. What is the population of Riverside?

Set up the proportion $\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.}$ Cross-multiplying gives $x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}$

Practice playeasy

Find the surface area of a sphere with radius $1$ . Use $\pi = 3$ .

$SA = 4 \pi r^{2} = 4 \times 3 \times 1 = 12$ .

Practice playeasy

A community pool is a rectangular prism $24$ feet long, $18$ feet wide, and $6$ feet deep when filled to the planned level. How many cubic feet of water does the pool hold at that level?

$V = \ell w h = 24 \times 18 \times 6 = 2{,}592$ cubic feet.

Practice playeasy

A ranch has $414$ cattle and a density of $18$ cattle per acre. What is the area of the ranch, in acres?

Set up the proportion $\dfrac{18\text{ cattle}}{1\text{ acre}} = \dfrac{414\text{ cattle}}{x\text{ acres}}\textsf{.}$ Cross-multiplying gives $18x = 414\textsf{,}$ so $x = 23\text{ acres}\textsf{.}$