F.2 Areas and Volumes (II)

2012-06-18 6:31 pm

1. A metallic cylinder of radius 10cm is melted and reformed to 2 smaller identical cylinders while the height is kept unchanged. Find the radius of a smaller cylinder

2. Can a square of area 32cm^2 be inscribed into a circle with radius 4cm? Briefly explain your idea.

回答 (1)

50418129

2012-06-18 7:15 pm

✔ 最佳答案

1.

let r cm be the radius of a small cylinder, thus

2(volume of small cylinder) = volume of large cylinder
2 x r^2 x pi x height of small cylinder = 10^2 x pi x height of large cylinder
2 x r^2 = 10^2
r^2 = 50
r = 5 sqrt 2

therefore, the radius of a small cylinder is 5 sqrt 2 cm

2.

when a square can inscribed into a circle,
the diagonal of the square <= diameter of the circle

let p cm be the diagonal of the square
2(p(p / 2)/2) = 32
p^2 = 64
p = 8

the diagonal of the square = 8
the diameter of the circle = 8
therefore, the square can inscribed into the circle

參考: knowledge

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