Given the similar pyramids pictured below.

The volume of pyramid 1 is 675 cm3 and its surface area is 504 cm2 If the volume of pyramid 2 is 3125 cm3 , what is its
surface area?

Question

07-03-2022
Mathematics

Answered

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Given the similar pyramids pictured below.

The volume of pyramid 1 is 675 cm3 and its surface area is 504 cm2 If the volume of pyramid 2 is 3125 cm3 , what is its
surface area?

Sagot :

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sqdancefan sqdancefan · Answer 1 · 2022-03-09T20:08:40-05:00

Answer:

1400 cm²

Step-by-step explanation:

The ratio of volumes of similar figures is the cube of the scale factor. Here, that is 3125/675 = sf³. That means the scale factor is ∛(3125/675) = 5/3.

The ratio of areas of similar figures is the square of the scale factor. Here, that is (5/3)² = 25/9.

The area of the larger pyramid is 25/9 times the area of the smaller one:

A = (25/9) × 504 cm² = 1400 cm²

The surface area of pyramid 2 is 1400 cm².

_____

Additional comment

You don't need to find the scale factor. You can jump directly to the fact that the surface area multiplier is the 2/3 power of the volume ratio.

Sagot :

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