F.2 Areas and volumes既問題

👨🏻‍🏫 學術台數學

Ka Lung

2010-05-08 5:21 am

以下有條問題,想請教大家:
20.The following is the information of a cylindrical glass of uniform thickness:
-Its outer diameter is 8 cm.
-its height is 10cm.
-its thickness is 0.5 cm.
(a) Find its capacity.
(b) Find the volume of material required for making the glass.

請注意:答呢條問題,必須有full step,我先會評佢為最佳答案.

更新1:

Remarks:請取答案至三個有效數字中文版問題: 20. 一厚薄均勻的圓柱形玻璃杯的外直徑為8cm,高為10cm,厚度為0.5cm. (a)求玻璃杯的容量. (b)求製迼這隻杯所需材料的體積.

回答 (3)

kennethtong

2010-05-08 6:40 am

✔ 最佳答案

玻璃杯的容量=(兀r^2)h
=(10-0.5)(4-0.5)^2兀
=9.5(3.5)^2兀
=366cm^3
製迼這隻杯所需材料的體積=(兀r^2)h-玻璃杯的容量
=16(10)兀-366
=503-366
=137cm^3

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風平浪靜海闊天空

2010-05-08 3:33 pm

圓柱體體積:兀(r^2)h
r=(8-0.5x2)/2=(8-1)/2=3.5
兀(r^2)=12.25兀=38.4845
兀(r^2)h=38.4845 x (10-0.5)

=365.603(cm^3)

製迼這隻杯所需材料的體積:

0.5x4x兀+8x兀*(10-0.5)=2x兀+76x兀=78x兀

=245.044(cm^3)

2010-05-08 07:34:40 補充：
001說的radius其實是diameter!!!

參考: me

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悪魔の去勢された雄羊の席〓はメェメェ

2010-05-08 5:32 am

(a) Capacity
=pi (8-0.5X2)^2 (10) (8-0.5x2=減左厚度之後既真正radius)
=490pi cm3

(b) Volume of material required for making the glass
=pi (8)^2 (10) - 490pi (用整個既vol-空心部分既vol,即係capcity)
=640pi - 490pi
=150pi cm3

參考: 自己

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收錄日期: 2021-04-23 22:04:19
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