Dimensions

[Guest]

A block of stone weighs 217 lbs. with the dimensions 20 in. in length, 15 in. in width, and 8 in. in thickness. Determine dimensions of another block weighing 13888 lbs.

Length * width * thickness = volume.

Unsure how to continue.

[Guest]

Note: the blocks are similar; sorry for omission error.

[Guest]

If the blocks are similar in shape then the volumetric dimensions ratio of the two will be the cubic ratio of the linear dimensions of the sides.

eg. for a 1 x 1 x 1 cube has volume of 1 cu.in then a 2 x 2 x 2 cube has volume of 8 cu.in

Ratio of sides 2 : 1 and Ratio of volumes 8 : 1

.................that should be a good pointer.....>>>>>>>>>>>>>>

[Guest]

20 * 15 * 8 = 2400 cu. in.

??

[Guest]

20 * 15 * 8 = 2400 cu. in. ......yes this is the volume of the small block.......maybe not really needed, it depends on your logical plan for solving the problem.

now.....how many of these smaller blocks will fit in the larger block...????????

[Guest]

13888 / 217 = 64

??

[Guest]

13888 / 217 = 64 .......Yes...OK.....so there are 64 small blocks in the large block.......OR we can say the the weight or volume of the large block is 64 times the smaller......OR the volume ratio of the large to the small is 64 to 1 ....written as..... 64:1

So all you have to do is find the ratio of the sides of the larger to the sides of the smaller

[Guest]

Smaller: 20" long, 15" wide, 8" thick

Larger: 1280" l , 960 " w , 512" t (times 64)

Not sure.

[Guest]

Smaller: 20" long, 15" wide, 8" thick

Larger: 1280" l , 960 " w , 512" t (times 64)

Not sure.

.............. What is your logic for doing this calculation......explain........?????....Did you not read the previous posts.....?????

[Guest]

" .............. What is your logic for doing this calculation......explain........?????....Did you not read the previous posts.....????? " Yes, I read them.

You said the ratio is 64:1, so I multiplied the smaller by 64 to obtain the larger.

[Guest]

Looks like you did not read them in detail and did not comprehend the contents......Here again are 2 of the earlier and very relevant posts.....

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If the blocks are similar in shape then the volumetric dimensions ratio of the two will be the cubic ratio of the linear dimensions of the sides.

eg. for a 1 x 1 x 1 cube has volume of 1 cu.in then a 2 x 2 x 2 cube has volume of 8 cu.in

Ratio of sides 2 : 1 and Ratio of volumes 8 : 1

.................that should be a good pointer.....>>>>>>>>>>>>>>
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13888 / 217 = 64 .......Yes...OK.....so there are 64 small blocks in the large block.......OR we can say the the weight or volume of the large block is 64 times the smaller......OR the volume ratio of the large to the small is 64 to 1 ....written as..... 64:1

So all you have to do is find the ratio of the sides of the larger to the sides of the smaller
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[Guest]

I don't know.

[Guest]

This is the example given in the post.................you need to follow the same type of workings

eg. for a 1 x 1 x 1 cube has volume of 1 cu.in then a 2 x 2 x 2 cube has volume of 8 cu.in

As a 2nd example, instead of a cube example we can use a rectangular block.......

eg. for a block with sides 2 in x 3 in x 4 in the volume will be 24 cu.ins and if the larger block has each side 3 times longer then its sides will be 6 x 9 x 12 giving a volume of 648 cu.ins. The ratio of the volumes of the the 2 blocks will be 648 to 24 OR 27 to 1 written as 27:1. But, the ratio of the lengths of the sides was 3 to 1 written 3:1

So for doubling (x2) the sides in the 1st example we had an increase of times 8 in volume

and in the 2nd example for a trebling (x3) of the sides we had an increase of times 27 in volume

2 is the cube root of 8 and 3 is the cube root of 27

So the ratios of the lengths of the sides is the cube root of the ratio of the volumes

So that is all you have to do to find the ratios of the lengths of the sides........you already know the ratio of the two volumes or ratio of weights (because weights are just volumes multiplied by a constant value to convert eg lbs/cu.in......and will cancel in ratio calculations.)

[Guest]

13888 / 27 = 64

Cube root of 64 = 4

20 * 4 = 80 (length)

15 * 4 = 60 (width)

8 * 4 = 32 (thickness)

80 * 60 * 32 = 153600 cu. in.

Not sure.

[Guest]

yes, correct ......ratio of the volumes (64:1) is the cube of the ratio of the corresponding sides (4:1)

[Guest]

Ok, thanks again.