Prism with Hollow Circular Section – Perimeter, Area & Surface Area
Prism with Hollow Circular Section – Perimeter, Area & Surface Area
Secondary 1
Diagram I shows the top view of a prism in which the shaded region represents the hollow part. Diagram II shows the prism of height \(16\) cm with a hollow cylindrical pipe being drilled through.
Given that \(PQ=5\) cm, \(QR=PS=5\) cm, \(PX=4\) cm, \(SR=11\) cm and \(SY=16\) cm.
The radius of the shaded circle is \(1.2\) cm. By taking \(\pi \) as \(3.142\), calculate
- the perimeter of the cross-sectional area as shown in Diagram I.
- the area of unshaded region in Diagram I.
- the total surface area of the prism in Diagram II.
- the volume of the material which is used to make this prism.
- the cost, correct to the nearest cent, to paint the total surface area of the prism, given that the cost for painting the prism is \(\$0.02\) for one square centimetre.
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Answer:(a) \(33.5\text{ cm}\) (3 s.f.) (b) \(27.5\text{ cm}^2\) (3 s.f.) (c) \(592\text{ cm}^2\) (3 s.f.) (d) \(440\text{ cm}^3\) (3 s.f.) (e) \(\$11.83\)
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