DC CAPE Geometry Circles Practice — Sports Academy Games

Circles skills

understand and apply theorems about circles

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).

Official sources

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

8 free questions · 0/0 correct

Practice playeasy

A rhombus has diagonals of length $6$ and $8$ . What is its area?

Area of a rhombus $= \dfrac{1}{2} \times d_{1} \times d_{2} = \dfrac{1}{2} \times 6 \times 8 = 24$ .

Practice playeasy

A sector of a circle has radius $4\text{ in}$ and central angle $60^{\circ}\textsf{.}$ What is the area of the sector?

The area of the whole circle is $\pi r^{2} = \pi \cdot 4^{2} = 16\pi\textsf{.}$ A $60^{\circ}$ sector is $\dfrac{60}{360} = \dfrac{1}{6}$ of the circle, so the area is $\dfrac{1}{6} \cdot 16\pi = \dfrac{8\pi}{3}\text{ in}^{2}\textsf{.}$

Practice playeasy

What is the length of a $180^{\circ}$ arc on a circle with radius $3\textsf{?}$

The circumference is $2\pi r = 2\pi \cdot 3 = 6\pi\textsf{.}$ A $180^{\circ}$ arc is $\dfrac{180}{360} = \dfrac{1}{2}$ of the circle, so the arc length is $\dfrac{1}{2} \cdot 6\pi = 3\pi\textsf{.}$

Practice playeasy

A right triangle has legs $6$ and $8$ . What is its area?

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

Practice playeasy

A sector of a circle has radius $6\text{ ft}$ and central angle $120^{\circ}\textsf{.}$ What is the area of the sector?

The area of the whole circle is $\pi r^{2} = \pi \cdot 6^{2} = 36\pi\textsf{.}$ A $120^{\circ}$ sector is $\dfrac{120}{360} = \dfrac{1}{3}$ of the circle, so the area is $\dfrac{1}{3} \cdot 36\pi = 12\pi\text{ ft}^{2}\textsf{.}$

Practice playeasy

What is the length of a $90^{\circ}$ arc on a circle with radius $2\textsf{?}$

The circumference is $2\pi r = 2\pi \cdot 2 = 4\pi\textsf{.}$ A $90^{\circ}$ arc is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the arc length is $\dfrac{1}{4} \cdot 4\pi = \pi\textsf{.}$

Practice playeasy

Find the area of a sector with radius $4$ and central angle $60°$ . Use $\pi = 3$ .

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

Practice playeasy

A sector of a circle has radius $10\text{ mm}$ and central angle $90^{\circ}\textsf{.}$ What is the area of the sector?

The area of the whole circle is $\pi r^{2} = \pi \cdot 10^{2} = 100\pi\textsf{.}$ A $90^{\circ}$ sector is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the area is $\dfrac{1}{4} \cdot 100\pi = 25\pi\text{ mm}^{2}\textsf{.}$