Question

The slant height and side length of the base of a square pyramid are in the ratio 2 : 1. If the total surface area is 500 cc, what is the value of the volume of the square pyramid?
1. 500 cm³
2. 645.5 cm³
3. 701 cm³
4. 812.2 cm³

Answer 1

Correct Answer - Option 2 : 645.5 cm³

Calculation:

Slant height and the side length of base are in the ratio 2 : 1.

∴ s = 2a

Total surface area = a² + 2as

⇒ 5a²

∴ 5a² = 500

⇒ a = 10 cm

If h is the height of a pyramid,

h² + (a/2)² = s²

⇒ h² = 15a²/4

⇒ h = 5√15 cm

Volume = a²h/3

⇒ (100 × 5√15)/3

⇒ 645.5 cm³