Step-by-step explanation:
The surface area of the resulting cuboid if 2 cubes each of volume 64 cm3 are joined end to end is 160 cm2
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.
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Step-by-step explanation:
The surface area of the resulting cuboid if 2 cubes each of volume 64 cm3 are joined end to end is 160 cm2
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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.