In a right prism with a square base, volume = 1024 cm³ and height = 16 cm. What is the side of the square base?

Correct — A.
Volume of a prism = base area × height.

Base area = 1024 ÷ 16 = 64 cm²
The base is a square, so side² = 64
Side = √64 = 8 cm → option (a)

Why the others are wrong

• (b)
  6 cm — 6 cm gives a base of 36 cm² and a volume of 36 × 16 = 576 cm³, well short of 1024 cm³.
• (c)
  10 cm — 10 cm gives a base of 100 cm² and a volume of 100 × 16 = 1600 cm³, well above 1024 cm³.
• (d)
  12 cm — 12 cm gives a base of 144 cm² and a volume of 144 × 16 = 2304 cm³, more than double the given 1024 cm³.

Every right prism has volume = base area × height, whatever the shape of its base. The height is the distance between the two identical end faces.

Here the base is a square, so base area = side². Divide the volume by the height to get the base area, then take the square root.

Check: a square prism 8 cm × 8 cm × 16 cm is two 8 cm cubes stacked, 2 × 512 = 1024 cm³.

Key facts

• Volume of a right prism = base area × height
• Lateral surface area of a right prism = base perimeter × height
• Square base of side a and height h: volume = a² × h
• √64 = 8 and 8³ = 512

Common traps

• Treating the prism as a cube and taking ∛1024 ≈ 10.08, which points to 10 cm
• Stopping at 1024 ÷ 16 = 64 and forgetting the square root

No directly related past PYQ was found.