2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Question

Infinity Learn · Accepted Answer

We will find the length of the edge of each cube by using the formula for the volume of a cube $$=$$ $$a3$$, where the length of the edge is 'a'.As the cubes are joined end to end, they will appear as follows:Using the formula for the surface of cuboid $$=$$ $$2(lb$$ $$+$$ bh $$+$$ $$lh)$$, where l, b, and h are length, breadth, and height respectively.Let the length of the edge of each cube be 'a'.Therefore, the volume of the cube $$=$$ $$a3The$$ volume of the cube, $$a3$$ $$=$$ $$64$$ $$cm3a3$$ $$=$$ $$64$$ $$cm3a$$ $$=$$ ∛$$(64$$ $$cm3)a$$ $$=$$ $$4$$ cmTherefore,Length of the resulting cuboid, l $$=$$ a $$=$$ $$4$$ cmBreadth of the resulting cuboid, b $$=$$ a $$=$$ $$4$$ cmHeight of the resulting cuboid, h $$=$$ $$2a$$ $$=$$ $$2$$ × $$4$$ cm $$=$$ $$8$$ cmSurface area of the resulting cuboid $$=$$ $$2$$ $$(lb$$ $$+$$ bh $$+$$ $$lh)=$$ $$2(4$$ cm × $$4$$ cm $$+$$ $$4$$ cm × $$8$$ cm $$+$$ $$4$$ cm × $$8$$ $$cm)=$$ $$2(16$$ $$cm2$$ $$+$$ $$32$$ $$cm2$$ $$+$$ $$32$$ $$cm2)=$$ $$2$$ × $$80$$ $$cm2=$$ $$160$$ $$cm2Thus$$, the surface area of the resulting cuboid is $$160$$ $$cm2$$.

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

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