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Question

Two identical cubes each of volume 64cm3 are joined together end to end. What is the surface area of the resulting cuboid?


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Solution

Calculating the surface area of the resulting cuboid:

Cube:

A three-dimensional figure which has six equal square faces is called a cube.

Cuboid:

A three-dimensional figure which has six rectangular faces is called a cuboid.

The side length of the cube is a.

Each faces in the cube is square.

Area of one squared surface=a2

Surface area of a cube=6a2

Since the two identical cubes joined together, it forms a cuboid

Calculating the surface area of the resulting cuboid:Surfaceareaoftheresultingcuboid=2(Surfaceareaofacube)-2(Areaofonesquaredsurface)Surfaceareaoftheresultingcuboid=26a2-2a2Surfaceareaoftheresultingcuboid=12a2-2a2Surfaceareaoftheresultingcuboid=10a2

Surface area of the resulting cuboid is 10a2...(1)

The volume of each cube is given as 64cm3.

Volume of cube

Volumeofcube=a3a3=64a=643a=4×4×43a=4

Substitute the value of a in (1):

Surfaceareaoftheresultingcuboid=1042Surfaceareaoftheresultingcuboid=10×16Surfaceareaoftheresultingcuboid=160

Hence, the area of the resulting cuboid is 160cm2.


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