Cuboid

The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?

Result

S =  238 cm2

Solution:

V=abc=245 245=5⋅ 7⋅ 7=5⋅ 72 a=5 b=7 c=7 S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (5⋅ 7+7⋅ 7+5⋅ 7)=238 cm2V=abc=245 \ \\ 245=5 \cdot \ 7 \cdot \ 7=5 \cdot \ 7^2 \ \\ a=5 \ \\ b=7 \ \\ c=7 \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (5 \cdot \ 7+7 \cdot \ 7+5 \cdot \ 7)=238 \ \text{cm}^2

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