# circle or sphere conversion/ratio

#### qazz

##### New member
want to convert mile measurement on a ball 8000 miles in diameter to inches on a ball 8.5 inches in diameter
ex: 200 miles distance on large ball to scale equivalent in inches on small ball. need formula for multiple distances

#### mmm4444bot

##### Super Moderator
Staff member
Hello qazz. Is this schoolwork?

#### qazz

##### New member
Hello qazz. Is this schoolwork?

no, ive been out of school for 43 yrs, lol this is for my hobby . to make scaled inlays for my product

#### Otis

##### Elite Member
Hi. By comparing diameters, we can obtain conversions factors. You'd like to know how much inch is needed on the small ball for each mile on the big ball, so we compare small to big.

$$\displaystyle \frac{8.5 \text{ inch}}{8000 \text{ mile}} = 0.0010625 \text{ inch per mile}$$

We multiply by that conversion factor, to scale miles to size.

200 [imath]\times[/imath] 0.0010625 = 0.2125

Therefore, a distance of 0.2125 inch (17/80ths) on the small ball represents 200 miles on the big ball.

If we were to compare large to small, instead, then we'd obtain a conversion factor telling us that every inch on the small ball represents about 941.17647 miles on the big ball.

Whatcha building? • Subhotosh Khan and qazz

#### lev888

##### Elite Member
no, ive been out of school for 43 yrs, lol this is for my hobby . to make scaled inlays for my product
Set up a proportion: 8.5 inches to 8000 miles as y inches to x miles
8.5 inches/8000 miles = y inches / x miles
y = ( (8.5 inches)/(8000 miles) ) * x
Convert to the same units and divide to get the conversion factor.

• Subhotosh Khan and qazz

#### qazz

##### New member
Hi. By comparing diameters, we can obtain conversions factors. You'd like to know how much inch is needed on the small ball for each mile on the big ball, so we compare small to big.

$$\displaystyle \frac{8.5 \text{ inch}}{8000 \text{ mile}} = 0.0010625 \text{ inch per mile}$$

We multiply by that conversion factor, to scale miles to size.

200 [imath]\times[/imath] 0.0010625 = 0.2125

Therefore, a distance of 0.2125 inch (17/80ths) on the small ball represents 200 miles on the big ball.

If we were to compare large to small, instead, then we'd obtain a conversion factor telling us that every inch on the small ball represents about 941.17647 miles on the big ball.

Whatcha building? i build custom pool cues, but working on a project for a friend,, u might have guessed, the 8000 miles is the earth. 8.5 is his project

• JayJay

#### Subhotosh Khan

##### Super Moderator
Staff member
i build custom pool cues, but working on a project for a friend,, u might have guessed, the 8000 miles is the earth. 8.5 is his project
The responses above converts lines (perimeter). Be careful about conversion of projected areas
..

• qazz