The surface area of a fish tank is 142 in2. The scale factor of a similar fish tank is larger by a scale factor of 6. What is the surface area of the larger fish tank?

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Surface area is proportional to the square of the linear scale factor.

Multiply 142 in^2 by 36 for your answer.

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To find the surface area of the larger fish tank, we can use the concept of similar shapes. When two shapes are similar, their corresponding sides are proportional to each other.

Let's assume the surface area of the smaller fish tank is S1, and the surface area of the larger fish tank is S2. The scale factor of the larger fish tank compared to the smaller fish tank is 6.

We know that the ratio of the surface areas of similar shapes is equal to the square of the ratio of their corresponding side lengths. In this case, if the scale factor of the larger fish tank is 6, then the ratio of their side lengths is 6:1.

Since the surface area is a 2-dimensional measurement, we need to square the scale factor to find the ratio of the surface areas. The ratio of the surface areas is 6^2:1^2, which simplifies to 36:1.

Now, we can set up a proportion to find the surface area of the larger fish tank:
S2/S1 = 36:1

Since we are given that the surface area of the smaller fish tank is 142 in², we can substitute S1 with 142 in²:
S2/142 = 36/1

Cross-multiplying the values:
S2 = 142 * (36/1)

Calculating the result:
S2 = 142 * 36 = 5112 in²

Therefore, the surface area of the larger fish tank is 5112 in².