how do i do this kind of math?

Question

i dont know what im supposed to do any help would br great

the problems are like

(word problems)

Jess made two picture frames. one frame is 8 in. by 14 in. the other frame is 12in. by 22 in. are the frames similar?

if the scale is 1 cm:8 m, how tall is the drawing of the 654-m skyscraper

a drawing of an airplane hanger was made useing a scale of 1 in. : 20ft. if the hangar is acually 250 feet wide how wide is the drawing

ALSO

tell weaher each scale reduces, enlarges, or preserves the size of the acual subject.

15 ft: 1 in

10mm: 1cm

2 m: 10 km


ALSO


An 8-cm cube is built from small cubes, each 1 cm on a side. compare the following values

The side lengths


The volumes




any help would be great

Answer 1

Jess made two picture frames. one frame is 8 in. by 14 in. the other frame is 12in. by 22 in. are the frames similar?

1 _______2

8in______12in

12in_____22in

if these were similar, theywould hav the same differenc between th sides (division not addition.)

these dont as 12/8 =1.5 and 22/12=1.83


if the scale is 1 cm:8 m, how tall is the drawing of the 654-m skyscraper

for evey 8meteres of the building, there is 1 cm of drawing

so the building is 654 high, and each 8 give one on paper

we divide 654 by 8 whivch equals 81.75 cm on paper

a drawing of an airplane hanger was made useing a scale of 1 in. : 20ft. if the hangar is acually 250 feet wide how wide is the drawing

each 20 ft give 1 in. 250/20=12.5 inches

ALSO

tell weaher each scale reduces, enlarges, or preserves the size of the acual subject.

15 ft: 1 in reduces - what was 15ft is now 1 in

10mm: 1cm preserves, 10mm is equal to 1cm so it stays the same size

2 m: 10 km enlarges, each 2m becomes 10km!


ALSO


An 8-cm cube is built from small cubes, each 1 cm on a side. compare the following values

altogether there are 512 *1 cm blocks, each of these has a side length of 6cm
512*6 = 3072
The side lengths
small=3071cm
large= 8*6=48cm

The volumes
each small cube has a volume of 1 cmcubed
=512 cubic cm

the large has a volume of 8*8*8
=512cubic cm

Answer 2

They seem ot be problems that are solved by the application of definitions. Definitions have to be learned or (if your memory is as bad as mine -- I hope not for your sake), you look them up every time.

'similar' in geometry means that the ratios are the same.

8 x 14 compared to 12 x 22.
The first one has an 'aspect' of 8/14 = 0.571428...
The second one has an aspect of 12/22 = 0.545454...
close (and "similar" in popular language) but not 'similar' in geometry jargon.
The other (and better) way to check is through the ratio of the (supposedly) similar elements. In this case lengths and widths.

widths: 8/12 = 2/3
lengths 12/22 = 6/11, not the same as 2/3.

One rectangle cannot be constructed by simply changing the scale of the other one.

12x21 would have been similar to 8x14. You get the larger one by making the small one 50% longer in both directions.
---

Scales: 1 cm in the drawing, represents 8 m of reality. Reality has 654 m (which is the same as 654/8 = 81.75 times 8 metres). Therefore, the drawing will be 81.75 times 1 cm = 81.75 cm = 0.8175 m.

The other way is to convert scale to a unit-less number; in this case you'd use the fact that one metre is 100 cm:

1 cm corresponds to 8 m = 800 cm

Scale = 1:800

To 'scale down' (go from reality to drawing) divide by 800.
To 'scale up' (from drawing to reality) multiply by 800.

Using a unit-free scale:
1 inch for 20 feet (20*12 = 240 inches)
scale = 1:240

Reality = 250 ft, drawing = 250 feet divided by 240 = 1.041666 feet (careful with the units: a unit-free scale does not change the units); 1.0416666*12= 12.5 inches.

Normally, a scale is given with the first number applying to the drawing and the second number applying to reality. For geographical maps (where the drawing is smaller than the country), they are normally of the type 1 inch = some large distance (or, if unit-free, 1 : x,xxx,xxx).

However, there are times when you want to make things bigger (a drawing of a living cell, for example). Then the bigger number comes first, or the second number is smaller than 1 (e.g., 1 cm = 5 microns)

So, if the first number is smaller, the drawing will reduce.
If the first number is bigger, the drawing will enlarge.
If both numbers are the same, size is preserved.

---

You will discover that it takes 8 smaller cubes to have the same length as the large cube, but a whole lot more to have the same volume.

Answer 3

The side lengths: 2 cm:1cm.

The volumes: 8cmcmcm: 1cmcmcm.

Answer 4

yes they are similar.

the drawing is 81.75 cm tall

12.5 in. (or 1 ft. 1/2 in.)

enlarges

preserves

reduces

1cm:8cm????