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Hey there! Ready to explore 3D space? Let's learn how we measure the room inside three-dimensional shapes!
Have you ever wondered how much water fits inside a bottle, or how many toys can pack into a box? That's what volume is all about! While area measures flat 2D space, volume measures the actual 3D space an object occupies.
In grade 8 we go past boxes to curved solids. A cylinder is really a circular base stacked h units tall, so its volume is V = πr²h, where r is the radius of that circular base.
Cones and spheres follow from the cylinder. A cone with the same base and height holds exactly one third as much, V = (1/3)πr²h, and a sphere with radius r has volume V = (4/3)πr³.
Find the volume of a cylindrical soup can with a radius of 3 inches and a height of 12 inches. Use π ≈ 3.14.
- Identify the formula for the volume of a cylinder: Volume = πr²h.
- Plug in the given dimensions: radius = 3 in and height = 12 in.
- Square the radius first: 3² = 9.
- Multiply by π and the height: 3.14 × 9 × 12 ≈ 339.12.
- Write your final answer with cubic units: about 339.12 cubic inches (or 339.12 in³).
