SOL Geometry Circles, Three-Dimensional Figures, and Measurement. Practice it free.

Students solve problems involving circles, solids, surface area, volume, and arc/sector measures. This Geometry reporting domain maps to 4 practice skills and 8 representative questions from the playable bank.

Geometry4 mapped skills
What the test measures

Circles, Three-Dimensional Figures, and Measurement skills

  1. circle theorems and properties

  2. surface area and volume

  3. area of circles and sectors

  4. three-dimensional figures

Standards basis

Virginia Mathematics Standards of Learning — Virginia

How the SOL reports it

Virginia SOL math is a state-specific assessment program built around the Virginia Mathematics Standards of Learning rather than a shared national test framework. It is aligned to Virginia grade-level and course standards, which are generally CCSS-like in organization but are published as Virginia-specific standards.

Blueprint & weighting

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

Practice by skill

Topics mapped to this domain

Surface area and volume

Grade 1015 questions

Volume word problems (ACT)

Grade 910 questions

Advanced area formulas

Grade 1015 questions

Perimeter and arc length

Grade 1015 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a cone with radius 33 and height 55. Use π=3\pi = 3.

V=13πr2h=13×3×9×5=45V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45.

Practice playmedium

A cylindrical rain barrel has an inside radius of 33 feet. After a storm, the water level rises 44 inches. What is the volume of the added water, in cubic feet?

Convert 44 inches to 13\dfrac{1}{3} foot. V=πr2h=π(3)2(13)=3πV = \pi r^{2} h = \pi (3)^{2}\left(\dfrac{1}{3}\right) = 3\pi cubic feet.

Practice playeasy

A triangle has sides 33, 44, and 55. What is its area?

This is a right triangle (33-44-55). Area =12×3×4=6= \dfrac{1}{2} \times 3 \times 4 = 6.

Practice playeasy

A triangle has sides 77, 1010, and 1212. What is its perimeter?

P=7+10+12=29P = 7 + 10 + 12 = 29.

Practice playeasy

Find the volume of a cylinder with radius 33 and height 22. Use π=3\pi = 3.

V=πr2h=3×9×2=54V = \pi r^{2} h = 3 \times 9 \times 2 = 54.

Practice playhard

A concrete drainage pipe is a hollow right circular cylinder. The outer radius is r1=6r_1 = 6 meters, the inner radius is r2=4r_2 = 4 meters, and the pipe is 55 meters long. What is the volume of concrete in the pipe wall, in cubic meters?

Wall volume is outer minus inner: V=πh(r12−r22)=π(5)(62−42)=π(5)(20)=100πV = \pi h(r_1^{2} - r_2^{2}) = \pi (5)(6^{2} - 4^{2}) = \pi (5)(20) = 100\pi cubic meters.

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 180°180° arc on a circle with radius 55. Use π=3\pi = 3.

L=180360×2πr=12×2×3×5=15L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 5 = 15.

Keep practicing

Turn circles, three-dimensional figures, and measurement into game time.

The SOL 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
7.G.B.6HSG.GMD.A.3HSG.C.B.5
Source and test overview
All SOL prepOfficial test source
Reporting categories

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