Find scale Factor:
[tex] (\cfrac{length_1}{length_2})^3 = \cfrac{volume_1}{volume_2} [/tex]
[tex] (\cfrac{length_1}{length_2})^3 = (\cfrac{125}{1000} ) [/tex]
[tex]\cfrac{length_1}{length_2} = \sqrt[3]{\cfrac{125}{1000} } [/tex]
[tex] \cfrac{length_1}{length_2} = \cfrac{5}{10} = \cfrac{1}{2} [/tex]
Find Surface area of the larger solid:
[tex] (\cfrac{length_1}{length_2} )^ 2=\cfrac{area_1}{area_2} [/tex]
[tex] (\cfrac{1}{2} )^ 2=\cfrac{150}{area_2} [/tex]
[tex] \cfrac{1}{4} =\cfrac{150}{area_2} [/tex]
[tex] area_2 = 150 \times 4 = 600 \text{ cm}^2 [/tex]
Answer: 600 cm²
