O-LevelMathematicsMensuration4024/21 · Oct/Nov 2019 · Q410 Marks

[Volume of cone = 1/3 πr²h] [Curved surface area of a cone = πrl] [Figure 4 Diagram of a gate post] The diagram shows a gate post. It is made in the shape of a cylinder with a cone on top. The cylinder and the cone each have diameter 8 cm. The height of the cylinder is 95 cm and the height of the cone is 15 cm.

(a)Calculate the volume of the gate post.[3]
(b)Show that the total curved surface area of the gate post is 2580 cm², correct to 3 significant figures.[5]
(c)A geometrically similar gate post has a total height of 150 cm. Calculate the total curved surface area of this gate post.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[3] 5030 or 5026 or 5027 or 5026.5 to 5027.2 M1 for 1/3 π × 4² × 15 M1 for π × 4² × 95 After 0 scored, SC1 for answer 20 100 or 20 110 or 20 106 to 20 109
[5] [l =] √15² + 4² (= √241) M2 M1 for [l =] 15² + 4² oe Curved surface area = 4π × √241 + π × 8 × 95 M2 M1 for 4 π × their√241 or π × 8 × 95 =2582.3 to 2583.03=2580 AG A1
[2] 4800 or 4797.5 to 4803.2 M1 for (150 / (95+15))² or (150/110)² soi

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