An office tower is shown in the attached diagram. it consists of a rectangular prism with a square base and a square based right pyramid.

a. calculate the height of the tower from the ground to the top of the roof's apex.

b. determine the volume of air inside the building, including the inside of the pyramid-shaped top.

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

The total volume of the building is

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