Question

2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3. The surface area of the smaller pyramid is 124 m^2. Determine each of the following, showing all your work and reasoning: find the surface area of the larger pyramid

Answer 1

Volume of square pyramid = a²h / 3

Surface area of square pyramid = a² +2a √((a²/4) + h²)

a = base edge 
h = height

for the large pyramid;
    volume = 648 m³
    height  = 24 m

Volume = a²h / 3
648 m³ = a² x 24 m / 3
       a²  = 81 m²
        a  = 9 m

by applying surface area equation to the large pyramid,
   surface area = a² +2a √((a²/4) + h²)
                        = 9² + 2 x 9 √((9² / 4 ) + 24²
                        = 520.53 m²

hence surface area of large pyramid = 520.53 m²

Answer 2

V  = a²h / 3

V = a²h / 3648 * 3 / 24= a²        a²  = 81       a  = 9
Area of square is 9 sq.m.

Area of the lateral sides of the larger pyramid:
a = 1/2 b*h
b = 9
h = sqrt (24^2 + 4.5^2) 
h = 24.42
a = 1/2 (9 * 24.42) = 109.88

SURFACE AREA = 4 lateral sides area + base area
SURFACE AREA = 4 * 109.88 + 9*9 = 520.53