Basic Mathematics05 marksNumerical: volume by cross sectionsVolume of solids of revolution
A pyramid 3 m3\text{ m}3 m high has a square base that is 3 m3\text{ m}3 m on a side. The cross section of the pyramid perpendicular to the altitude x mx\text{ m}x m down from the vertex is a square x mx\text{ m}x m on a side. Find the volume of the pyramid.
A pyramid 3 m3\text{ m}3 m high has a square base that is 3 m3\text{ m}3 m on a side. The cross section of the pyramid perpendicular to the altitude x mx\text{ m}x m down from the vertex is a square x mx\text{ m}x m on a side. Find the volume of the pyramid. [5]
- Height of pyramid: $h = 3$ m - Square base: $3$ m on a side - Cross section at distance $x$ m down from the vertex: a square that is $x$ m on a side - Cross-section side length as function of $x$: side $= x$ - Integration limits: from vertex $x = 0$ to base $x = 3$ Step 1: Cross-sectional area ...