Question

Match the following surface areas of the cubes with the length of their respective sides:

• A. 8 units
• B. 4 units
• C. 1 unit
• D. 3 units

Answer 1

Surface area of a cube of side length ${}^{\prime }{a}^{\prime }=6a^2$

54 sq. units:
$6a^2=54\Rightarrow a^2=9=3\times 3\Rightarrow a=\sqrt{9}=3$

Hence, length of a cube of surface area 54 sq. units is 3 units.

6 sq. units:
$6a^2=6\Rightarrow a^2=1=1\times 1\Rightarrow a=\sqrt{1}=1$

Hence, length of a cube of surface area 6 sq. units is 1 unit.

384 sq. units:
$6a^2=384\Rightarrow a^2=64=8\times 8\Rightarrow a=\sqrt{64}=8$

Hence, length of a cube of surface area 384 sq. units is 8 units.

96 sq. units:
$6a^2=96\Rightarrow a^2=16=4\times 4\Rightarrow a=\sqrt{16}=4$

Hence, length of a cube of surface area 96 sq. units is 4 units.