有冇人可以幫我解答以下一些數學問題??>.

2008-08-25 10:15 am

1.)The surface area of a sphere is equal to the total surface area of a hemisphere.If the ratio of the radius of the sphere to that of the hemisphere is 1:k,find the value of k.(correct you answer to s significant figures.)
2.)Fiona deposits $19200 in a bank for two and a half years at an interest rate of 3%p.a. compounded half-yearly.What is the interest earned by Fiona???(correct your answer to 2 dcimal places)
3.)At present,2400m2 of a sea-bed is enclosed by coral.If the area of enclosure has increased by 4%each year,find the area of the sea-bed enclosed by coral 10 years ago.(correct your answer to the nearest 0.1m2)
連式呀5該~>.<

回答 (1)

NCY

2008-08-26 10:27 pm

✔ 最佳答案

1)the surface area of a sphere = 4πr2
the total surface area of a hemisphere = (1 / 2)(4πr2) + πr2
surface area of ratio
= 4πr2 : (1 / 2)(4πr2) + πr2
= 4πr2 : 2πr2 + πr2
= 4πr2 : 3πr2
= 4 : 3
ratio of the radius = √4 : √3 = 2 : √3
ratio of the radius of the sphere to that of the hemisphere is 1 : k
So k = √3 / 2

2)the time of two and a half years = 2 X 2.5 = 5
the interest rate = 3% / 2 = 1.5%
the amount after two and a half years
= principal X (1 + interest rate)time
= $19200 X (1 + 1.5%)5
= $20684 (correct to the nearest)
the interest earned by Fiona
= amount﹣principal
= $20684﹣$19200
= $1484 (correct to the nearest)

3)the area of the sea-bed enclosed by coral 10 years ago
= the original value X (1 + percentage)time
= 2400 X (1 + 4%)10
= 3552.6m2 (correct to the nearest 0.1m2)

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