Discussion

Question:

The Volume of a pyramid with a square base is 200 cubic cm. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

Explanation:

Let the side of the square base AB = BC = CD = DA = ‘a’.

Height OB = 13.

​​​​​​​

Volume of a square base pyramid = a² × h/3 = 200 cm³

⇒ a² = 600/13

Diagonal AC = a√2

⇒ AB = a/√2

In right ∆OAB, AO² = AB² + OB²

⇒ AO² = (a/√2)² + 13²

⇒ AO² = a²/2 + 169

⇒ AO² = 300/13 + 169 = 2497/13

⇒ AO ≈ 13.86

Thus, the length of the slant slope (when rounded to the nearest integer) = 14 cm

Hence, option (c).

» Your doubt will be displayed only after approval.