A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume

Analyze the question: We need the volume of a pyramid with a rectangular base of 12 m by 8 m and a height of 14 m.

Concept: The volume of any pyramid is one-third of the base area times the perpendicular height:

V = ⅓ × (base area) × h

Solution:

1. Base area = 12 × 8 = 96 m²
2. Volume = ⅓ × 96 × 14
3. 96 ÷ 3 = 32
4. 32 × 14 = 448

So V = 448 m³

Checking the options:

• A. 322 m³ is not equal to 448.
• B. 448 m³ matches our working.
• C. 632 m² is wrong, and its unit is wrong, since volume is in m³ and not m².
• D. 840 m² is also wrong, with the wrong unit. Note that 96 × 14 ÷ 1.6 is not a meaningful route. Forgetting the ⅓ would give 1344, which isn't here either.

(Options C and D are written as m², which looks like a typo in the question, but it doesn't affect the answer.)

Tip: The pyramid (and cone) formula always carries a ⅓. Think of it as "one-third of the matching prism": a prism with the same base and height would hold 96 × 14 = 1344 m³, and the pyramid holds exactly a third of that. Also, always check units: volume is in cubic units (m³).