A design on a balloon is 2 cm wide when the balloon holds 47 cm^3. How much must the balloon hold for the design to be 6 cm wide? I'm confused about how to solve this. Could someone please show me the steps?
length scale change is 3/1
volume changes as cube of length
Therefore 3*3*3 = 27 times
so
27*47= 1269 cm^3
Thank you so much!
To solve this problem, you can use the concept of proportional reasoning. Here's how you can approach it:
Step 1: Determine the ratio of the width to the volume.
The design width is 2 cm, and the volume is 47 cm^3. Therefore, the ratio of width to volume is 2 cm / 47 cm^3.
Step 2: Determine the volume required for a width of 6 cm.
To find the volume required for a width of 6 cm, we can set up a proportion using the ratio obtained in Step 1.
Let x be the volume required for a width of 6 cm.
The ratio for the new width and volume is 6 cm / x.
Setting up the proportion: 2 cm / 47 cm^3 = 6 cm / x.
Step 3: Cross-multiply and solve for x.
Cross-multiplying gives us: (2 cm)(x) = (6 cm)(47 cm^3).
Now, we can solve for x: 2x = 6 * 47 cm^3.
Simplifying further: 2x = 282 cm^3.
Dividing both sides by 2: x = 141 cm^3.
Therefore, to have a design width of 6 cm, the balloon must hold 141 cm^3.