Question

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

Answer 1

Answer:

Step-by-step explanation:

Given 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 degree with the lower base.

We have a1 = 19 cm, a2 = 7 cm, angle L = 60 degree

Area of bottom base

A1 = a1^2 = 19^2 = 361 sq cm

A2 = a2^2 = 7^2 = 49 sq cm

Now to find altitude we have  

h = tan 60 x a1/2 – a2/2

 = tan 60 x 19/2 – 7/2

= √3 x 12/2

h = 10.39 cm

Now to find volume we have

V = h/3 x a1 + a2 + √a1 x a2

V = 10.39/3 x (361 + 49 + √ 361 x 49 )

V = 3.4633 x 543

V = 1880.59 cm^3

So volume is 1880.59 cm^3