Volume and surface area of solids

Japanese school year: Junior high 1

What you learn

Learn the formulas to calculate the volume and surface area of pyramids, cones, and spheres. This topic builds on previous knowledge of prisms, cylinders, and circles. These skills are essential for solving real-world 3D geometry problems, such as determining capacity and designing spatial models.

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Key points

This formula is used to calculate the volume $V$ of a pyramid or cone. It multiplies the base area $S$ by the height $h$ , and divides by $3$ (one third the volume of a cylinder or prism).

V = \frac{1}{3}Sh

This formula is used to calculate the surface area $S$ of a sphere with radius $r$ . It equals $4$ times the area of a circle with the same radius ( $\pi r^2$ ).

S = 4\pi r^2

This formula is used to calculate the volume $V$ of a sphere with radius $r$ . It is found by multiplying $\frac{4}{3}$ by $\pi$ and the cube of the radius ( $r^3$ ).

V = \frac{4}{3}\pi r^3

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Practice 1Coming soon