Answer:
248.5 mm³
Explanation:
Given similar shapes with a smaller : larger surface area ratio of 95 mm² : 245 mm², you want the larger volume if the smaller is 60 mm³.
Scale factor
The scale factor for the two shapes is the square root of the ratio of areas:
larger : smaller = √(245 : 95) ≈ 1.60591
The ratio of volumes is the cube of the scale factor for the two shapes:
larger volume : smaller volume = (1.60591 : 1)³ ≈ 4.14156 : 1
Then the larger volume is ...
larger volume = smaller volume × 4.14156 = (60 mm³)(4.14156)
larger volume ≈ 248.5 mm³
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Additional comment
You don't need to compute the actual scale factor. The ratio of volumes is the 3/2 power of the ratio of areas. That fact is used in the calculation shown in the attachment.
<95141404393>