SOL Geometry Circles, Three-Dimensional Figures, and Measurement Practice

What the test measures

Circles, Three-Dimensional Figures, and Measurement skills

circle theorems and properties
surface area and volume
area of circles and sectors
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).

Official sources

Virginia Department of Education
VDOE — Standards of Learning for Mathematics (2023 SOL grade/course standards and assessment blueprints)
VDOE — SOL Test Blueprints (per-reporting-category item counts live inside the individual grade/EOC blueprint PDFs)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

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 playeasy

A triangle has sides $3$ , $4$ , and $5$ . What is its area?

This is a right triangle ( $3$ - $4$ - $5$ ). Area $= \dfrac{1}{2} \times 3 \times 4 = 6$ .

Practice playeasy

A sector of a circle has radius $8\text{ yd}$ and central angle $90^{\circ}\textsf{.}$ What is the area of the sector?

The area of the whole circle is $\pi r^{2} = \pi \cdot 8^{2} = 64\pi\textsf{.}$ A $90^{\circ}$ sector is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the area is $\dfrac{1}{4} \cdot 64\pi = 16\pi\text{ yd}^{2}\textsf{.}$

Practice playeasy

A triangle has sides $7$ , $10$ , and $12$ . What is its perimeter?

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

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?