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 area of a 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, volume of the cube = a3 Volume of the cube, a3 = 64 cm3 a3 = 64 cm3 a = ∛(64 cm3) a = 4 cm Therefore, Length of the resulting cuboid, l = a = 4 cm Breadth of the resulting cuboid, b = a = 4 cm Height of the resulting cuboid, h = 2a = 2 × 4 cm = 8 cm Surface 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 cm2 Thus, the surface area of the resulting cuboid is 160 cm2.
Answers
Answer:
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid
Solution:
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:
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid
Using the formula for the surface area of a 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, volume of the cube = a3
Volume of the cube, a3 = 64 cm3
a3 = 64 cm3
a = ∛(64 cm3)
a = 4 cm
Therefore,
Length of the resulting cuboid, l = a = 4 cm
Breadth of the resulting cuboid, b = a = 4 cm
Height of the resulting cuboid, h = 2a = 2 × 4 cm = 8 cm
Surface 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 cm2
Thus, the surface area of the resulting cuboid is 160 cm2.
Step-by-step explanation:
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