Question

(Answer with steps please)

Skateboarders use half pipes for doing tricks A half-pipe is similar to a half cylinder which is not enclosed on the ends.

a. Explain how you could manipulate the surface area formula for a cylinder to calculate the curved surface area of the half pipe.

b. To the nearest square metre, calculate the curved surface area of the half pipe if it is 9 m long?

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Answer 1

Explanation:

a). Total surface area of cylinder is defined by sum of curved surface area and surface area of the top and bottom.

Total surface area = 2πrh + 2πr²

Skateboarders use a half pipe structure which are not closed at the ends.

Therefore, curved surface of the half pipe =
`(2\pi rh)/(2)`

= πrh

b). If r = 2.5 m and h = 9 m,

Curved surface area of the half pipe = π(2.5)(9)

= 70.69 m²

≈ 71 m²