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Circles & spheres

Basic shapes

Japanese school year: Elementary 3

What you learn

Learn the geometric properties of circles and spheres by focusing on centers, radii, and diameters. These round shapes are essential in understanding wheels, clock faces, sports balls, and compass drawings. Prior familiarity with length measurement and basic solid shapes will provide the necessary foundation for understanding this topic.

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Key points

This formula finds the diameter d of a circle or sphere. The diameter is twice the radius r.

d=2rd = 2r

This equation shows the rule of a circle or sphere. The distance from center O to any point P is always radius r.

OP=rOP = r

This formula finds the volume V of a sphere. Multiply radius r by itself three times, then multiply by pi π and 4/3.

V=43πr3V = \frac{4}{3}\pi r^3

This formula finds the surface area S of a sphere. Multiply radius r by itself, then multiply by pi π and 4.

S=4πr2S = 4\pi r^2

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