Circle and solids, grade 8

Eighth-grade circles and solids.Subjects

The topics, in order:

the circle: its circumference and the area of a disc;
the cylinder: its net, surface area and volume;
the cone: its slant height, volume and surface area;
Pythagoras’ theorem in space: the diagonal of a box, the height of a cone and of a pyramid.
Learning lessons explain a topic with examples, and have a few questions to try.
Practice lessons are all questions.
Go in order.

How the page works: Using a page.

Last updated on 18.10.2026

Formulas: circle and solids, grade 8

The number pi – the value to calculate with
$\displaystyle \pi\approx3.14$
The circumference of a circle – $\displaystyle d$ the diameter
$\displaystyle C$ $\displaystyle =$ $\displaystyle \pi d$
The circumference of a circle – $\displaystyle r$ the radius
$\displaystyle C$ $\displaystyle =$ $\displaystyle 2\pi r$
The area of a disc
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2$

The curved surface area – $\displaystyle r$ the radius of the base, $\displaystyle h$ the height
$\displaystyle L$ $\displaystyle =$ $\displaystyle 2\pi r h$
The surface area – the two bases and the curved surface
$\displaystyle A$ $\displaystyle =$ $\displaystyle 2\pi r^2+2\pi r h$
The volume – the base area times the height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \pi r^2 h$

The slant height $\displaystyle l$ – the hypotenuse of a triangle whose legs are the radius $\displaystyle r$ and the height $\displaystyle h$
$\displaystyle l^2$ $\displaystyle =$ $\displaystyle r^2+h^2$
The curved surface area
$\displaystyle L$ $\displaystyle =$ $\displaystyle \pi r l$
The surface area – the base and the curved surface
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2+\pi r l$
The volume – a third of the cylinder with the same base and height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{\pi r^2 h}{3}$

The diagonal of a box $\displaystyle d$ – $\displaystyle a$ , $\displaystyle b$ , $\displaystyle c$ its three edges
$\displaystyle d^2$ $\displaystyle =$ $\displaystyle a^2+b^2+c^2$
In a square pyramid – $\displaystyle k$ the height of a side face, $\displaystyle h$ the pyramid’s height, $\displaystyle a$ the side of the base
$\displaystyle k^2$ $\displaystyle =$ $\displaystyle h^2+\left(\frac{a}{2}\right)^2$