What shape is half of an American football prolate spheroid when cut in half on the short side? Is this a type of cone?
When an American football prolate spheroid is cut in half on the short side, it forms two identical shapes known as oblate spheroids. An oblate spheroid is a three-dimensional shape that resembles a flattened sphere, with its equatorial diameter being greater than its polar diameter.
Unlike a cone, which has a circular base and a single vertex, an oblate spheroid does not have a vertex. Instead, it has two rounded ends and a smooth, continuous surface. Mathematically, an oblate spheroid can be described by the equation ( \frac{x^2 + y^2}{a^2} + \frac{z^2}{b^2} = 1 ), where (a ) and (b) are the lengths of the equatorial and polar diameters, respectively.
Related Questions:
- What is the shape of a cross-section of an American football prolate spheroid perpendicular to its long axis? A circle
- What is the volume of an oblate spheroid? ( \frac{4}{3} \pi a^2 b )
- What is the surface area of an oblate spheroid? ( 2 \pi a^2 + \pi b^2 )
- Give an example of an oblate spheroid that occurs in nature. The Earth
- Can an oblate spheroid be formed by rotating an ellipse around its major axis? Yes
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