Use the disk method to verify that the volume of a right circular cone is (1/3)π r2h, where r is the radius of the base and h is the height.

Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = x² + y2…

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Q: Region R Let R be the region bounded by the graphs of y = VT, y = e, and the y-axis.

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Q: Find the largest volume of a rectangular box inscribed in a cone of base radius r and the height h.

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Q: Find the area of the portion of the sphere of radius 10 (centered at the origin) that is in the cone…

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Q: Find the volume of the torus formed by revolving the circle x2 + y2 = a2 about the line x = b(b >…

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Q: Find the volume of the solid whose base is the circle x² + y² = 49 and the cross sections…

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Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant…

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Q: Q: A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular…

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Q: Ex3: Find the volume bounded by the surface z = 3 – x - y and the area in x-y plane enclosed by the…

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Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

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Q: n the mid-20th century, engineers constructed a series of canals to move irrigation water from water…

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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.