Question

A Babushka doll is a nesting doll where each doll is exactly similar to the ones that fit inside of it, as well as the ones that fit around it. If a Babushka doll with a surface area of 200 has a volume of 180, what would be the volume of a similar Babushka doll with a surface area of 180? Round your answer to three decimal places.

Answer 1

To calculate the volume of a smaller Babushka doll with a given surface area, we determine the scale factor from the surface area ratio and apply it to the power of 1.5 to the original volume to find the new volume.

Step-by-step explanation:

The question involves dimensional analysis and the concept of scaling volumes and surface areas in similar geometric shapes. Since the volumes and surface areas of similar shapes increase proportionally, we can use the given surface areas and volume of one Babushka doll to calculate the volume of another with a different surface area.

For similar objects, if the scale factor for the surface area (SA) is k, then the scale factor for volume (V) is k to the power of 1.5 (because volume is a three-dimensional measure while surface area is two-dimensional). Therefore, if the original doll has a surface area of 200 and a volume of 180, and we want to find the volume of a doll with a surface area of 180, we calculate the scale factor k = 180/200 = 0.9. We then apply the scale factor to the volume: New Volume = 180 * 0.9^(1.5), which gives us the new volume of the smaller Babushka doll.