Question

The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?

Answer 1

The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?​

we have that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.

so

Find the scale factor

ratio volumes=40.5/12=3.375

3.375=(scale factor)^3

`\text{scale factor=}\sqrt[3]{3.375}`

scale factor=1.5

To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon

so

1.5*(10)=15 inches

the answer is 15 inches