Final answer:
To find the surface area of the larger vase with a height of 13 cm when combined with a smaller vase totaling 1800 cm², we use proportional ratios based on their heights. The area of the larger vase is found to be 1170 cm².
Step-by-step explanation:
The subject of the question is to find the surface area of one of two similar vases with different heights, given that the total surface area for both is 1800 square cm. The heights of the vases are 9 cm and 13 cm. Since the vases are similar, their surface areas will be proportional to the square of their linear dimensions (heights in this case).
Let's denote the surface area of the smaller vase (height of 9 cm) by A1 and the surface area of the larger vase (height of 13 cm) by A2. The total surface area is A1 + A2 = 1800 cm². Using the ratio of the heights squared (because surface area is a two-dimensional measure and so varies with the square of the linear dimensions), we get (9/13)² = A1/A2.
Solving these equations simultaneously gives us the values for A1 and A2. The surface area A2 of the larger vase can be calculated to be 1170 cm².