The ratio of the corresponding linear measures of two similar cans of vegetables is 2 to 3. The smaller can has a surface area of 180 square

Question

The ratio of the corresponding linear measures of two similar cans of vegetables is 2 to 3. The smaller can has a surface area of 180 square centimeters. Find the surface area of the larger can.

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Rose 3 weeks 2021-12-29T03:40:00+00:00 1 Answer 0 views 0

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    2021-12-29T03:41:10+00:00

    The surface area of the larger can is 405 square centimeter

    Solution:

    The ratio of the corresponding linear measures of two similar cans of vegetables is 2 to 3

    The smaller can has a surface area of 180 square centimeters

    Let the surface area of larger can be “x”

    Area is a square measurement

    Therefore to find the ratio of the areas, we need to square the ratio of the linear measurements

    (\frac{2}{3})^2 = \frac{4}{9}

    Therefore, area and above ratio is in proportion

    \frac{4}{9} = \frac{180}{x}\\\\4x = 180 \times 9\\\\4x = 1620\\\\x = 405

    Thus surface area of the larger can is 405 square centimeter

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