If the slant height of a right pyramid with a square base is 4 meter a

1.	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» 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.

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»

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.