A farm grain silo is made from a cylinder of radius 3 m and height 6 m, topped with a cone of the same radius and height 2.5 m, as shown. 3 m6 m2.5 m© EAGLE...
Question 1 Report
A farm grain silo is made from a cylinder of radius 3 m and height 6 m, topped with a cone of the same radius and height 2.5 m, as shown.
- Work out the volume of the cylindrical part, in terms of \(\pi\). (2)
- Work out the volume of the conical part, in terms of \(\pi\). (2)
- Work out the total volume of the silo, to 3 significant figures. (1)
Answer Details
The silo is a composite solid, so its total volume is the cylinder's volume plus the cone's volume, each found from its own standard formula using the shared radius.
- \(V_{\text{cyl}}=\pi\times3^2\times6\) [1 mark]; \(=54\pi\) m\(^3\) [1 mark]
- \(V_{\text{cone}}=\dfrac13\pi\times3^2\times2.5\) [1 mark]; \(=7.5\pi\) m\(^3\) [1 mark]
- Total \(=54\pi+7.5\pi=61.5\pi=193\) m\(^3\) (3 s.f.) [1 mark]
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