Two cubes with each side b are joined to form a cuboid What is the surface area of this - Maths - Visualising Solid Shapes

Question

Two cubes with each side b are joined to form a cuboid What is the
surface area of this cuboid? What will be the surface area of the
arrangement when another cuboid of same length is added?

Shruti Tyagi · Accepted Answer

Dear student,

We have,Each sides of cube i e, length, breadth and height=bWhen 2 cubes are joined to form a cuboidLength of cuboid=b+b=2bBreadth of cuboid=bHeight of cuboid=bNow, surface area of cuboid=2lb+bh+lh=22b×b+b×b+2b×b=22b2+b2+2b2=2×5b2=10b2Thus the surface area of cuboid formed by joining two cubes=10b2

Now, Length of new cuboid=2b+2b=4bBreadth of new cuboid=bHeight of new cuboid=bSurface area of cuboid=2lb+bh+lh=24b×b+b×b+4b×b=24b2+b2+4b2=2×9b2=18b2Thus the surface area of the arrangement when another cuboid of same length is added=18b2 Regards

Two cubes with each side b are joined to form a cuboid. What is the surface area of this cuboid? What will be the surface area of the arrangement when another cuboid of same length is added?