1(a). A metallic right cylinder with both base radius and height of 10cm is melted, 1/3 of the metal is recast to form a right circular cone with the base same as orginal cylinder. Find the height of the cone. ans.10
(b) The remaining metal is recast to form another right circular cone with the base same as the orginal cylinder. Find the total surface arear of this cone. ans.1020
F3 Mensuration. be quick
2010-06-29 3:48 am
回答 (2)
2010-06-29 4:33 am
✔ 最佳答案
1a.) Let h be the heigh [ 兀(10)^2 X10 ] X 1/3 = 1/3兀(10)^2 X h
333+1/3 兀 = 33+1/3 (兀)(h)
10= h
1b.)Let h be the heigh
[ 兀(10)^2 X10 ] X 2/3 = 1/3兀(10)^2 X h
666+2/3 兀 = 33+1/3 兀(h)
20= h
Let l be the length: 10^2 + 20^2 = l^2
開方500 = l
total surface area of the cone = 兀(10)(開方500) + 兀(10)^2
= 1016.40738(cor to 3 sig = 1020)
參考: me
2010-06-29 4:13 am
a)
The volume of the right cylinder=[pi(10)^2]*10=1000pi cm^3
The volume of the right circular cone=(1000pi/3) cm^3
(1/3)pi(base radius)^2*(heigth)=1000pi/3
(1/3)pi(10)^2*(heigth)=1000pi/3
heigth=10cm
b)
The volume of the remaining metal=(2/3)*1000pi=2000pi/3 cm^3
(1/3)pi(10)^2*(height)=2000pi/3
height=20cm
Total surface area
=pi*10*(sq root(10^2+20^2))+pi*(10)^2
=(100sqrt5+100)pi
=1020cm^2 (correct to the 3 sig. fig.)
2010-06-29 00:07:32 補充：
Remark: The side area of a right circular cone=pi*r*l, where l is the slant height of the cone.
2010-06-29 13:34:47 補充：
#1 l²=r²+h²
#2 pi=π
The volume of the right cylinder=[pi(10)^2]*10=1000pi cm^3
The volume of the right circular cone=(1000pi/3) cm^3
(1/3)pi(base radius)^2*(heigth)=1000pi/3
(1/3)pi(10)^2*(heigth)=1000pi/3
heigth=10cm
b)
The volume of the remaining metal=(2/3)*1000pi=2000pi/3 cm^3
(1/3)pi(10)^2*(height)=2000pi/3
height=20cm
Total surface area
=pi*10*(sq root(10^2+20^2))+pi*(10)^2
=(100sqrt5+100)pi
=1020cm^2 (correct to the 3 sig. fig.)
2010-06-29 00:07:32 補充：
Remark: The side area of a right circular cone=pi*r*l, where l is the slant height of the cone.
2010-06-29 13:34:47 補充：
#1 l²=r²+h²
#2 pi=π
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