WebApr 10, 2024 · We can obtain a sphere by revolving half a circle about the x x -axis. This circle can be parameterized as x (t)=r\cos (t) x(t) = rcos(t) and y (t) = r\sin (t) y(t) = rsin(t) for 0 \leq t \leq \pi 0 ≤ t≤ π. From this, we get … WebDetermine the cross-section area of the given cylinder whose height is 25 cm and radius is 4 cm. Solution: Given: Radius = 4 cm Height = 25 cm We know that when the plane cuts the cylinder parallel to the base, then the …
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WebVolume of a spherical sector = (2/3)πR 2 h, where, R is radius of sphere, h is height. Volume of a spherical segment = (1/6)πh (3R 12 + 3R 22 + h 2 ), where, R 1 1 is base … WebFeb 19, 2024 · 2 - The area of the cross section of the sphere, and every cross section parallel to it, is. Each cross section of the cylinder with two cones removed is the shape … how far is buford ga from stone mountain ga
How is the cross-sectional area of a sphere calculated?
Web1 Answer. You have two equations: x 2 + y 2 + z 2 = 1 and x + y + z = k. The coordinates here relate to your new coordinates as follows: The first two columns are your u 1 and u 2, the last is the normal vector of the plane. Now use this to … WebUse the formula that the area of a disk of radius r is πr2: the area of the cross section is cross section at x = π(√1 − x2)2 = π(1 − x2) Then integrate this from − 1 to + 1 to get the volume: volume = ∫right left area of cross-sectiondx = ∫ + 1 − 1π(1 − x2)dx = π[x − x3 3] + 1 − 1 = π[(1 − 1 3) − ( − 1 − ( − 1)3 3)] = 2 3 + 2 3 = 4 3 Exercises WebSep 19, 2024 · Cross-sectional area is determined by squaring the radius and then multiplying by 3.14. For example, if a tree is measured as 10″ DBH, the radius is 5″. Multiplying 5 by 5 equals 25, which when multiplied by 3.14 equals 78.5. Thus, the cross-sectional area of a 10″ DBH tree is 78.5. how far is buhl from twin falls