Question

Part 1: Create and provide the dimensions for two similar figures of your choosing.
Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume?
Part 3: Show your work, either using the actual volumes or using the formula, that the volume ratio is true.

THIS IS MY ANSWER. please let me know if it is correct.

PART 1: Two cubes are similar, cube A has a height of 64in, width of 64in, and length of 64in. Cube B has a height of 25in, width of 25in, and length of 25in.

PART 2: The similarity to these ratios of their surface area and volume is 8:5.

PART 3: Cube A has a volume of 262,144 inches cubed and cube B has a volume of 15,625 inches cubed. Cube A has a surface area of 24,576 inches cubed and cube B has a surface area of 3,750 inches cubed. So when you simplify it all the way out the ratio of cube A to cube B is 8:5.

Answer 1

As I understand it, the ratio of the dimensions is 8 to 5. But not the surface area or volume. Not sure if that was what you are asking or not...

Answer 2

The ratio of volumes is 262144/15625, or about 16.777216 to 1.
The ratio of surface areas is 24576/3750, or about 6.5536 to 1.

Answer 3

what if i changed the dimensions of each cube?
like cube ! is 8 by 8 by 8 and cube be 5 by 5by 5

Answer 4

PART 1: Two cubes are similar, cube A has a height of 8in, width of 8in, and length of 8in. Cube B has a height of 5in, width of 5in, and length of 5in.

PART 2: The similarity to these ratios of their surface area and volume is 8:5.

PART 3: Cube A has a volume of 512 inches cubed and cube B has a volume of 125 inches cubed. Cube A has a surface area of 384 inches cubed and cube B has a surface area of 150 inches cubed. So when you simplify it all the way out the ratio of cube A to cube B is 8:5.
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is this right?

Answer 5

well, then the ratio of the volumes would be something like 512 to 125.

Answer 6

And surface area is in inches squared, not inches cubed.

Answer 7

simply put, \[\frac{8}{5}\neq \frac{ 512 }{ 125 }\]

Answer 8

Okay, so lets try this for a 3rd time.
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PART 1: Two cubes are similar, cube A has a height of 8in, width of 8in, and length of 8in. Cube B has a height of 5in, width of 5in, and length of 5in.

PART 2: The similarity to these ratios of their volume is 512:125 and their surface area is 384:150.

PART 3: Cube A has a volume of 512 inches cubed and cube B has a volume of 125 inches cubed. Cube A has a surface area of 384 inches squared and cube B has a surface area of 150 inches squared.

Answer 9

Hmm yeah I guess. This is kind of a weird question. What class is it for?

Answer 10

I know.... And geometry, the chpater im doing is surface and lateral area, and volume

Answer 11

Ok... I never did this. have fun.