If the slant height of a right pyramid with square base is 4 metre and the total slant surface of the pyramid is 12 square metre,

Question

If the slant height of a right pyramid with a square base is 4 meter and the total slant surface of the pyramid is 12 square meter, then the ratio of total slant surface and area of the base is :

(a) 16 : 3 

(b) 24: 5 

(c) 32: 9

(d) 12 : 3

Answer 1

Answer: (a) = 16:3

Slant surface or Lateral surface area of a pyramid

=\(\frac{1}{2}\) × Perimeter of base × Slant height

Given, 12 =  \(\frac{1}{2}\) × 4 × a × 4

where, each side of the square = a metres

⇒ \(a = \frac{24}{16} =\frac{3}{2}\) m.

∴ Area of base = \(\big(\frac{3}{2}\big)^2\, m^2 = \frac{9}{4}\, m^2\)  

∴  Reqd. ratio = 12 : \(\frac{9}{4}\)  

= 16:3.