Q21 of 48 Page 13

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


Concept Used: Surface Area of cube = 6a2


Volume of Cube = a3


Surface area of cuboid = 2 (lb + bh + hl)


Volume of cuboid = lbh


Where a = edge of cube, l = length of the cuboid, b = breadth of the cuboid, and h = height of the cuboid.


Given: Volume of cubes = 64 cm3


Explanation:


Let us find the edge of the cube first.


Volume of the cube = 64 cm3


a3 = 64 cm3


a = (64 cm3)1/3


a = 4 cm


Now when the cubes are joined, new dimensions are,


Length of the cuboid = 8 cm


Breadth of the cuboid = 4 cm


Height of the cuboid = 4 cm


Now putting these values in the formula of volume of cuboid we get,


Surface Area of cuboid = 2(8×4 + 4×4 + 4×8)


Surface Area of cuboid = 2(32 + 16 + 32)


Surface Area of cuboid = 160 cm2


Volume of cuboid = lbh


Volume of cuboid = 8 × 4 × 4


Volume of cuboid = 128 cm3


Hence, the surface area of resulting cuboid is 160 cm2 and volume of resulting cuboid is 128 cm3.


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