As viewed from above, a swimming pool has the shape of the ellipse x^2/4900+y^2/2500=1 where x and y are measured in feet. The cross sections perpendicular to the x-axis are squares. Find the total volume of the pool.

As viewed from above, a swimming pool has the shape of the ellipse x^2/4900+y^2/2500=1 where x and y are measured in feet. The cross sections perpendicular to the x-axis are squares. Find the total volume of the pool.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

Question

As viewed from above, a swimming pool has the shape of the ellipse

x^2/4900+y^2/2500=1

where x and y are measured in feet. The cross sections perpendicular to the x-axis are squares. Find the total volume of the pool.

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