If the length of the diagonal of a cube is 16
3
cm, what is its lateral surface area (in sq cm)?
- A2,048
- B3,072
- C1,024
- D1,536
Solution & Step-by-step Explanation
Let the edge of the cube be scm.
The formula for the diagonal of a cube is given by:
Diagonal=s
3
Given that the diagonal is 16
3
cm:
s
3
=16
3
⟹s=16cm
The formula for the lateral surface area (LSA) of a cube is:
LSA=4s
2
Substituting the value of s:
LSA=4×(16)
2
=4×256=1,024cm
2
The formula for the diagonal of a cube is given by:
Diagonal=s
3
Given that the diagonal is 16
3
cm:
s
3
=16
3
⟹s=16cm
The formula for the lateral surface area (LSA) of a cube is:
LSA=4s
2
Substituting the value of s:
LSA=4×(16)
2
=4×256=1,024cm
2