S3. MATHS HELP

2013-01-06 7:49 am

Q.30 A metallic sphere of radius 10 cm is melted and recast into 2 small spheres of equal radii. The radius of the small spheres is 7.93700526 cm. What is the percentage change in total surface area?
A. -50% B. -37.0% C. 26.1% D. 41.4%
Answer is C.求過程

Q.31 A spherical orange has diameter 6 cm. If its peel is 5 mm thick, what is the volume of the peel?
A. 26.8 cm³ B. 44.8 cm³ C. 47.6 cm³ D. 79.6 cm³
Answer is C.求過程

Q.36 A boiling tube is composed of a cylindrical part and a hemispherical part. The surface area of the boiling tube is 24兀 cm². When 8兀 cm³ of solution is poured into the tube, what is the depth of solution in the tube?
圖片參考：http://imgcld.yimg.com/8/n/HA01113436/o/20130105234133.jpg
A. 20/3 cm B. 22/3 cm C. 23/3 cm D. 25/3 cm
Answer is B.求過程

回答 (1)

胡雪8°

2013-01-06 9:28 am

✔ 最佳答案

Q.30
The total surface area of the original sphere
= 4π(10)² cm²
= 400π cm²

The total surface area of the two small spheres
= 2 x 4π(7.93700526)² cm²
= 504π cm²

Percentage change in total surface area
= [(504π - 400π)/400π] x 100%
= 26%
≈ 26.1%

The answer is : C. 26.1%

******
Q.31
Volume of the whole orange
= (4/3)π(6/2)³ cm³
= 36π cm³

Volume of the internal part (other than the peel) of the orange
= (4/3)π[(6/2)- 0.5] cm³
= 62.5π/3 cm³

Volume of the peel
= 36π - (62.5π/3) cm³
= 47.6 cm³

The answer is : C.47.6 cm³

*****
Q.36
Volume of the hemispherical part
= (1/2) x (4/3) x π x (1)³ cm³
= 2π/3 cm³

Height of the solution in the cylindrical part
= [8π - (2π/3)] / [π(1)²] cm
= 22/3 cm

The answer is : B. 22/3 cm

參考: 胡雪

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