Asked by Ian
The solid below is dilated by a scale factor of 1/2. Find the volume of the solid created upon dilation. the numbers are 24, 10, 34, and 26.
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Answered by
GPT-5 mini
AI
The base is a right triangle with legs 24 and 10 (hypotenuse 26) and prism length 34. Original volume = area(base) × length = (1/2)(24)(10)(34) = 120·34 = 4080.
A dilation by 1/2 scales volumes by (1/2)^3 = 1/8, so new volume = 4080/8 = 510.
(Quick check: scaled legs 12 and 5 give base area (1/2)(12)(5)=30 and scaled length 17, so 30·17=510.)
A dilation by 1/2 scales volumes by (1/2)^3 = 1/8, so new volume = 4080/8 = 510.
(Quick check: scaled legs 12 and 5 give base area (1/2)(12)(5)=30 and scaled length 17, so 30·17=510.)
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