Answer to Question #162059 in Trigonometry for Reem

Question

Find the volume of a frustum of a regular square pyramid if the base edges are 7 cm and 19 cm, and one lateral edge is inclined at an angle of 60 degrees with the lower base.

 

Answer 1

Volume of a frustrum = Volume of the larger pyramid - Volume of the smaller pyramid

V = 1/3(BASE AREA*HEIGHT) - 1/3(base area*height)

Please follow the attached image for guidance

sin 45⁰ = x₁cm/19

x₁cm = 19*sin 45⁰ = 13.44 cm

Now calculating the H, Height of the larger pyramid we have;

Tan 60⁰ = H/13.44

H = 13.44 *Tan 60⁰ = 23.28 cm

sin 45⁰ = x₂cm/7

x₂cm = 7*sin 45⁰ = 4.95 cm

Now calculating the h, Height of the larger pyramid we have;

Tan 60⁰ = h/4.95

h = 4.95 *Tan 60⁰ = 8.57 cm

Therefore the volume of the frustrum is calculated as below;

(1/3*19²*23.28) - (1/3*7²*8.57)

2801.36 - 139.98

V = 2661.38 cm³