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Volume and surface area of spheres, cylinders, cones, boxes and pyramids.

Volume formulas come in families: a prism or cylinder is base × height, a pyramid or cone is a third of that, and a sphere is 4/3 πr³. Every solid here is rendered in 3D. Drag to rotate it.

ຕົວຢ່າງ​ທີ່​ໄດ້​ເຮັດ · volume of a sphere with radius 3

Geometry · Solids

Volume of a sphere with radius 3

ຂັ້ນ​ຕອນ​ຕໍ່​ຂັ້ນ​ຕອນ

  1. r = 3

    Sphere.

  2. V = \tfrac{4}{3}\pi r^3 = 36 \pi \approx 113.10

    Volume.

  3. S = 4\pi r^2 = 36 \pi \approx 113.10

    Surface area.

ເປີດ​ເຜີຍ​ຄຳ​ຕອບ
V = 36 \pi \approx 113.10,\quad S = 36 \pi

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ລົງທະບຽນ ចូល

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ວິທີການ: Solids

  1. Sphere.
  2. Volume.
  3. Surface area.

ຄໍາຖາມທີ່ຄົນຖາມ

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

ເພີ່ມເຕີມໃນ Geometry

TrianglesPythagorean theoremCirclesPolygonsCoordinate geometryEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres