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The volume of a cube is 216 cm³. What is its surface area?
216 cm²
144 cm²
36 cm²
108 cm²
216 cm²
Calculate the side length using the cube root of the volume, then substitute it directly into the surface area formula 6a2.
Volume of the cube V = 216 cm³
V=a3
Calculate the side length using the cube root of the volume, then substitute it directly into the surface area formula 6a2.
Confusing the formulas for volume and surface area or multiplying the volume by 6 directly instead of finding the side length first.
Find the side length of the cube
The volume of a cube is given by V=a3. Given V=216 cm3, we find the side length a by taking the cube root.
a=3216=6 cm
Calculate the total surface area
The surface area of a cube with side length a is given by 6a2. Substituting a=6 cm gives the final result.
SA=6×(6)2=6×36=216 cm2
A is correct because the side length of the cube is 6 cm, which calculates to a total surface area of 216 cm².
Mensuration questions in competitive exams frequently test the interplay between linear dimensions, surface area, and volume.