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[andante]

MathIzzzFun:

andante:

I have come across the following question which is Pei Hwa 2009 Prelim Paper 1 Q29, however I think the model answer given as 360 is not correct. Pls advise.


Clement had a wooden block measuring 50 cm by 70 cm by 90 cm. He wanted to cut out some little cuboids mesauring 2 cm by 3 cm by 4 cm. What was the minimum amount of wood wasted ?

In fact, I found discussion on this question, someone show the working for 360 cm3 and some suggested 180 cm3 but I thought that the answer can be even smaller than that.

Thanks.

Hi andante,

here's how I did it

http://i55.tinypic.com/ht7ng1.jpg\">

cheers.

Why do you cut into 35x11x30 but not 35x12x30 ?
If I cut it into 35x12x30 and further cut the rest into 22x23x1, I will have 4cm3 left, not sure whether it is correct.

BTW, this question needs to explore all possibilities in order to know which is the minimum and if it is so, then I think it is no demanding and too much for the little mark awarded.

Pls advise.

[MathIzzzFun]

andante:

MathIzzzFun:

[quote=\"andante\"]I have come across the following question which is Pei Hwa 2009 Prelim Paper 1 Q29, however I think the model answer given as 360 is not correct. Pls advise.


Clement had a wooden block measuring 50 cm by 70 cm by 90 cm. He wanted to cut out some little cuboids mesauring 2 cm by 3 cm by 4 cm. What was the minimum amount of wood wasted ?

In fact, I found discussion on this question, someone show the working for 360 cm3 and some suggested 180 cm3 but I thought that the answer can be even smaller than that.

Thanks.

Hi andante,

here's how I did it

http://i55.tinypic.com/ht7ng1.jpg\">

cheers.

Why do you cut into 35x11x30 but not 35x12x30 ?
If I cut it into 35x12x30 and further cut the rest into 22x23x1, I will have 4cm3 left, not sure whether it is correct.

BTW, this question needs to explore all possibilities in order to know which is the minimum and if it is so, then I think it is no demanding and too much for the little mark awarded.

Pls advise.[/quote]Hi andante,

50 cm x 70 cm x 90 cm / (2 cm x 3 cm x 4 cm) = 13125 blocks. So, it is not possible to have 4 cm3 left over.

When it is cut into 35x12x30 blocks, the block left is 2 cm x 90 cm x 70 cm, with this block, can only cut into 1 x 30 x 17 blocks leaving behind a block of 2 cm x 90 cm x 2 cm block ie 360 cm3.

cheers.

[andante]

MathIzzzFun:

Hi andante,


50 cm x 70 cm x 90 cm / (2 cm x 3 cm x 4 cm) = 13125 blocks. So, it is not possible to have 4 cm3 left over.

When it is cut into 35x12x30 blocks, the block left is 2 cm x 90 cm x 70 cm, with this block, can only cut into 1 x 30 x 17 blocks leaving behind a block of 2 cm x 90 cm x 2 cm block ie 360 cm3.

cheers.

Hi,
When it is first cut into 35x12x30 blocks, the block left is 2x90x70, that is right. But there are two ways to cut it. your solution of 360cm3 is one of the ways. The second way to cut it will generate 22x23x1 block i.e. 90 cut into 22x4 with remaining of 2cm and 70 cut into 23x3 with remaining of 1 cm which produces wastage of 1x2x2 = 4cm. (hope that I did not miss it anything)

[MathIzzzFun]

andante:

MathIzzzFun:

Hi andante,


50 cm x 70 cm x 90 cm / (2 cm x 3 cm x 4 cm) = 13125 blocks. So, it is not possible to have 4 cm3 left over.

When it is cut into 35x12x30 blocks, the block left is 2 cm x 90 cm x 70 cm, with this block, can only cut into 1 x 30 x 17 blocks leaving behind a block of 2 cm x 90 cm x 2 cm block ie 360 cm3.

cheers.

Hi,
When it is first cut into 35x12x30 blocks, the block left is 2x90x70, that is right. But there are two ways to cut it. your solution of 360cm3 is one of the ways. The second way to cut it will generate 22x23x1 block i.e. 90 cut into 22x4 with remaining of 2cm and 70 cut into 23x3 with remaining of 1 cm which produces wastage of 1x2x2 = 4cm. (hope that I did not miss it anything)

Hi andante,

when the remaining block is cut into 22 x 23 x 1 blocks, the remaining wood consists of an L-shaped block which can be cut into two blocks as shown. The wastage would be 456 cm3.

http://i52.tinypic.com/34zhw81.jpg\">


cheers.

[andante]

MathIzzzFun:

andante:

[quote=\"MathIzzzFun\"]Hi andante,


50 cm x 70 cm x 90 cm / (2 cm x 3 cm x 4 cm) = 13125 blocks. So, it is not possible to have 4 cm3 left over.

When it is cut into 35x12x30 blocks, the block left is 2 cm x 90 cm x 70 cm, with this block, can only cut into 1 x 30 x 17 blocks leaving behind a block of 2 cm x 90 cm x 2 cm block ie 360 cm3.

cheers.

Hi,
When it is first cut into 35x12x30 blocks, the block left is 2x90x70, that is right. But there are two ways to cut it. your solution of 360cm3 is one of the ways. The second way to cut it will generate 22x23x1 block i.e. 90 cut into 22x4 with remaining of 2cm and 70 cut into 23x3 with remaining of 1 cm which produces wastage of 1x2x2 = 4cm. (hope that I did not miss it anything)

Hi andante,

when the remaining block is cut into 22 x 23 x 1 blocks, the remaining wood consists of an L-shaped block which can be cut into two blocks as shown. The wastage would be 456 cm3.


cheers.[/quote]Hi,
Oh... I see. Just wondering how one knows the proposed 24cm3 is the minimum ? need to explore all possibilities ?

Thx

[MathIzzzFun]

andante:

MathIzzzFun:

[quote=\"andante\"]
Hi,
When it is first cut into 35x12x30 blocks, the block left is 2x90x70, that is right. But there are two ways to cut it. your solution of 360cm3 is one of the ways. The second way to cut it will generate 22x23x1 block i.e. 90 cut into 22x4 with remaining of 2cm and 70 cut into 23x3 with remaining of 1 cm which produces wastage of 1x2x2 = 4cm. (hope that I did not miss it anything)

Hi andante,

when the remaining block is cut into 22 x 23 x 1 blocks, the remaining wood consists of an L-shaped block which can be cut into two blocks as shown. The wastage would be 456 cm3.


cheers.

Hi,
Oh... I see. Just wondering how one knows the proposed 24cm3 is the minimum ? need to explore all possibilities ?

Thx[/quote]Hi andante,

50 cm x 70 cm x 90 cm / (2 cm x 3 cm x 4 cm) = 13125 blocks, so if there should be any wastage, it will be a multiple of 24cm3 (2cm x 3cm x 4cm). Thus, the minimum wastage is 24cm3.

cheers.

[Chan09]

Dear all,

Need help
1) ratio of angsana tree to coconut tress was 1:4. When 30 coconut trees were chopped down to make way for an additional 25 angsana trees, the difference between the no. of angsana trees and coconut trees became 14. How many angsana trees were there in the beginning?
Ans: 23 angsana trees

2) the ratio of the length of a rectangle to its breath is 5:7. If the perimeter is 48cm, find the area of the rectangle?
Ans: 140

[Maize]

Hi Maths Guru


I am not able to solve this question given by my daughters school:I hope u can help!

" After saving for a month, 1/5 of Heidi’s savings was equal to 3/7 of Joseph’s savings.
After Heidi spent $356 and Joseph saved an additional $428 , they had a n equal amount in their savings. How much did Heidi and Joseph save together in the end?"

[Suz855]

1) ratio of angsana tree to coconut tress was 1:4. When 30 coconut trees were chopped down to make way for an additional 25 angsana trees, the difference between the no. of angsana trees and coconut trees became 14. How many angsana trees were there in the beginning?



[][][][][]Angsana[][][][][] Coconut \t\t
B4\t\t\t1u\t\t4u
change\t\t\t+25\t\t-30
after\t\t\t1u+25\t\t4u-30

4u-30-1u-25 =14
3u =69
1u =23 (Angsana)

2) the ratio of the length of a rectangle to its breath is 5:7. If the perimeter is 48cm, find the area of the rectangle?

2x (5u+7u) =24u
24u–> 48
1u –> 2

Area of rect –> 10 x 14 = 140cm2

[MathIzzzFun]

Maize:

Hi Maths Guru


I am not able to solve this question given by my daughters school:I hope u can help!

\" After saving for a month, 1/5 of Heidi's savings was equal to 3/7 of Joseph's savings.
After Heidi spent $356 and Joseph saved an additional $428 , they had a n equal amount in their savings. How much did Heidi and Joseph save together in the end?\"

Hi

hope this helps

http://i51.tinypic.com/2r3v1qr.jpg\">

cheers.