Composite Cross-Section: Trapezium with Semi-Circular Cut-Out
Composite Cross-Section: Trapezium with Semi-Circular Cut-Out
Secondary 1
The diagram shows the uniform cross-section of a solid paper weight \(ABCDE\), which is in the shape of a trapezium with a semi-circular hole \(ABC\) cut out of it. It is given that \(AC\) is parallel to \(DE\), \(AC=7\) cm, \(CD=15\) cm, \(DE=21\) cm, \(AE=13\) cm, and the height of the trapezium is \(12\) cm.
- Find the area of \(ABCDE\).
- The length of the prism is \(30\) cm. Calculate its
- volume.
- surface area.
- The prism is melted down and recast into a cylinder of radius \(8\) cm. Find the height of the cylinder.
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Answer:(a) \(149\text{ cm}^2\) (3 s.f.) (b)(i) \(4460\text{ cm}^3\) (3 s.f.) (b)(ii) \(2100\text{ cm}^2\) (3 s.f.) (c) \(22.2\text{ cm}\) (3 s.f.)
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