2 Maths Questions (about ratio)

HappyFred

2007-01-04 8:44 am

1. The volume of a cylinder is ６４ｍ3 . If the height of the cylinder is 8.8m, find the height of a similar cylinder of volume ３４３ｍ3 .

2. The base areas of two similar cones are ３２ｃｍ2 and ５０ｃｍ2 .
(a) Find the ratio of the curved surface area of the smaller cone to that of the larger one.
(b) Find the volume of the larger cone if that of the smaller cone is ２８８ｃｍ3 .

回答 (1)

Rinka

2007-01-04 9:25 am

✔ 最佳答案

1 ,
you have to apply the formula
V1/V2 = (L1/L2)^3
for similar object

V1 = 64 , L1 = 8.8
V2 = 343 , L2 = ?
V1/V2 = (L1/L2)^3
64/343 = (8.8/L2)^3
4 / 7 = 8.8 / L2
L2 = 15.4 m

2(a) ,
ratio in base area = ratio in surface area
( 或者咁講 , 相同部份的area比例是一樣的 )
ratio of curved surface area = 32 / 50
ratio of curved surface area = 16 / 25

2(b)
A1/A2 = (L1/L2)^2
16 / 25 = (L1/L2)^2
L1/L2 = 4 / 5 ..........(1)

V1/V2 = (L1/L2)^3
288 / V2 = ( 4 / 5 ) ^3 ....................(by (1))
288 / V2 = 64 / 125
V2 = 562.5 cm^3

👍 0 👎 0