A cube has 6 faces (top, bottom, and 4 sides).
Each face is a square with area a2.
Total surface area =6×a2
=6a2
(A) matches with (III)
The volume formula for any pyramid is:
Volume =31×(area of base)×height
(B) matches with (IV)
A circular ring is the region between two circles.
The larger circle has radius R and the smaller circle has radius r.
Area =πR2−πr2
=π(R2−r2)
(C) matches with (I)
For a square with side a, using the Pythagorean theorem:
diagonal2=a2+a2
diagonal2=2a2
diagonal=2a2
=a2
(D) matches with (II)
The correct matching is:
(A) - (III), (B) - (IV), (C) - (I), (D) - (II)