F3 Maths Area and Volume?

2016-12-25 9:27 pm

The funnel section of a ventilation shaft in an air-conditioning system is a frustum of a rectangular pyramid as shown. How much air is trapped inside the funnel ？

回答 (1)

用戶2053

2016-12-27 10:58 am

✔ 最佳答案

Let AP meet BQ at T , then TP : TA = PS : AD
(TA - 20) : TA = 15 : 20
1 - 20/TA = 3/4
20/TA = 1/4
TA = 80 cm

The height of the rectangular pyramid with the base ABCD = √(80² - (30/2)²) = 5√247 cm
The volume of the rectangular pyramid = (1/3)(20×30)(5√247) = 1000√247 cm³

The volume of the frustum of the rectangular pyramid
= 1000√247 - PQRST
= 1000√247 - 1000√247 (PS/AD)³
= 1000√247 - 1000√247 (3/4)³
= 1000√247 (1 - 27/64)
= 4625√247 / 8
= 9085.947576 cm³

∴ There are 4625√247 / 8 = 9085.947576 cm³ air is trapped inside the funnel.

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