DC CAPE Geometry Circles. Practice it free.

This domain focuses on circle properties, equations, and relationships. This Geometry reporting domain maps to 2 practice skills and 8 representative questions from the playable bank.

GeometryCircles2 mapped skills
What the test measures

Circles skills

  1. understand and apply theorems about circles

  2. find arc lengths and areas of sectors

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).

Practice by skill

Topics mapped to this domain

Advanced area formulas

Grade 1015 questions

Perimeter and arc length

Grade 1015 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

A rhombus has diagonals of length 66 and 88. What is its area?

Area of a rhombus =12×d1×d2=12×6×8=24= \dfrac{1}{2} \times d_{1} \times d_{2} = \dfrac{1}{2} \times 6 \times 8 = 24.

Practice playeasy

Find the arc length of a 90°90° arc on a circle with radius 66. Use π=3\pi = 3.

L=90360×2πr=14×2×3×6=9L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 6 = 9.

Practice playeasy

A right triangle has legs 66 and 88. What is its area?

Area =12×6×8=24= \dfrac{1}{2} \times 6 \times 8 = 24.

Practice playeasy

Find the arc length of a 180°180° arc on a circle with radius 33. Use π=3\pi = 3.

L=180360×2πr=12×2×3×3=9L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 3 = 9.

Practice playeasy

Find the area of a sector with radius 44 and central angle 60°60°. Use π=3\pi = 3.

Sector area =60360×πr2=60360×3×16=8= \dfrac{60}{360} \times \pi r^2 = \dfrac{60}{360} \times 3 \times 16 = 8.

Practice playeasy

Find the arc length of a 90°90° arc on a circle with radius 22. Use π=3\pi = 3.

L=90360×2πr=14×2×3×2=3L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 2 = 3.

Practice playeasy

A triangle has sides 55, 1212, and 1313. What is its area?

This is a right triangle (55-1212-1313). Area =12×5×12=30= \dfrac{1}{2} \times 5 \times 12 = 30.

Practice playeasy

A semicircle has radius 1010. Its curved edge has length kπk\pi. What is the value of kk?

Half the circumference is 12⋅2π⋅10=10π\dfrac{1}{2} \cdot 2 \pi \cdot 10 = 10\pi, so k=10k = 10.

Keep practicing

Turn circles into game time.

The DC CAPE placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.C.B.5
The same skills on other tests
ATLASMCAPMO MAPNY State Math
Source and test overview
All DC CAPE prepOfficial test source
Reporting categories

More Geometry domains

CongruenceThis domain measures understanding of congruence and similarity in geometric figures.8 QsPractice →Similarity, Right Triangles, and TrigonometryThis domain covers similarity, right triangle relationships, and trigonometric ratios.8 QsPractice →Expressing Geometric Properties with EquationsThis domain addresses coordinate geometry and equations describing geometric relationships.8 QsPractice →Geometric Measurement and DimensionThis domain covers measurement of two- and three-dimensional figures.8 QsPractice →Modeling with GeometryThis domain focuses on using geometry to solve modeling problems.8 QsPractice →