The cost of making a hollow metal sphere with outer radius r cm is $ C. It is given that c is a sum of two parts, one part is a constant and the other part varies directly as the cube of r. When r = 2, C = 124; When r = 3, C = 181.
a) Find the cost of making a hollow metal sphere with outer radius 5 cm.
b) If the cost is $ 475 and the thickness of the sphere is 1 cm, find the volume of metal to mike this sphere.
variations?
2016-06-15 8:35 am
回答 (1)
2016-06-15 11:53 am
✔ 最佳答案
(a)Suppose C(r) = a + br^3
C(2) = a + b*2^3 = a + 8b = 124 ..... (1)
C(3) = a + b*3^3 = a + 27b = 181 ..... (2)
(2) - (1) , we have
19b = 57 , so b = 3 , substitute into (1)
a = 124 - 8b = 124 - 8*3 = 100 , hence :
C(r) = 100 + 3*r^3
C(5) = 100 + 3*5^3 = 475
(b)
By (a) , outer radius = 5
inner radius = 5 - 1 = 4
V
= (4/3)*π*5^3 - (4/3)*π*4^3
= (4/3) π * ( 5^3 - 4^3 )
= (4/3) π * 61
= ( 244 / 3 ) π
Ans :
(a) $475
(b) ( 244 / 3 ) π
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