Question

The volumes of two similar solids are 125 cm^3 and 1,000 cm^3. The surface area of the smaller solid is 150 cm^2. What is the surface area of the larger solid?
275 cm^2

300 cm^2

375 cm^2

600 cm^2

Answer 1

Find scale Factor:

$(\cfrac{length_1}{length_2})^3 = \cfrac{volume_1}{volume_2}$

$(\cfrac{length_1}{length_2})^3 = (\cfrac{125}{1000} )$

$\cfrac{length_1}{length_2} = \sqrt[3]{\cfrac{125}{1000} }$

$\cfrac{length_1}{length_2} = \cfrac{5}{10} = \cfrac{1}{2}$

Find Surface area of the larger solid:

$(\cfrac{length_1}{length_2} )^ 2=\cfrac{area_1}{area_2}$

$(\cfrac{1}{2} )^ 2=\cfrac{150}{area_2}$

$\cfrac{1}{4} =\cfrac{150}{area_2}$

$area_2 = 150 \times 4 = 600 \text{ cm}^2$

Answer: 600 cm²