Answer:
[tex]\boxed{\text{a. 111.1 m; b. 56 575 m}^{3}}[/tex]
Step-by-step explanation:
a. Height
(i) Height of prism
The height of the prism is 70 m.
(ii) Height of pyramid
Consider the red triangle in the diagram.
The diagonal of the square base is given by
d² = a² + a² = 2a²
d² = 2(26)² = 2 ×676 = 1352 m²
d = √1352 = 36.77 m
The base of the triangle R is
R = ½d = ½ × 36.77 = 18.38 m
Now,
h² + R² = e²
h² + 18.38² = 45²
h² + 338 = 2025
h² = 1687
h = 41.07 m
(iii) Total height
Total height = height of prism + height of pyramid = 70 + 41.07 = 111.1 m
b. Volume
(i) Volume of prism
V = lwh
V = 70 × 26 × 26 = 47 320 m³
(ii) Volume of pyramid
The formula for the volume of a square pyramid is
V = ⅓a²h
V = ⅓ × 26² × 41.07 = 9255 m³
(iii) Total volume
Total volume = volume of prism + volume of pyramid
V = 47320 + 9255 = 56 575 m³
The total height of the building is [tex]\boxed{\textbf{111.1 m}}[/tex]
The total volume of the building is [tex]\boxed{\textbf{56 575 m}^{3}}[/tex]
