A cook has a set of four mixing bowls with lids. The bowls stack inside each other and are similar to each other. The surface areas of the two largest bowls are 2300 cm? and 1100 cm?. The scale factor is the same from each bowl to the next smaller bowl. Estimate the surface areas of the two smaller bowls.

Question

A cook has a set of four mixing bowls with lids. The bowls stack inside each other and are similar to each other. The surface areas of the two largest bowls are 2300 cm? and 1100 cm?. The scale factor is the same from each bowl to the next smaller bowl. Estimate the surface areas of the two smaller bowls.

Answer 1

Let's denote the scale factor as x.

Surface area of the largest bowl = 2300 cm²
Surface area of the second largest bowl = 1100 cm²

Using the scale factor, we can set up the following equation:

(2300 cm²) / x = 1100 cm²

Solving for x:
2300 / x = 1100
x = 2300 / 1100
x = 2.09

So, the scale factor is approximately 2.09.

Now, we can use this scale factor to estimate the surface areas of the two smaller bowls:

Surface area of third largest bowl = 1100 cm² / 2.09 ≈ 526.8 cm²
Surface area of smallest bowl = 526.8 cm² / 2.09 ≈ 252.3 cm²

Therefore, the estimated surface areas of the two smaller bowls are approximately 526.8 cm² and 252.3 cm².