Question

The volume of the frustum of regular triangular pyramid is 135 m3. The lower base is an equilateral triangle with an edge of 9 m. The upper base is 8 m above the lower base. What is the upper base edge, in m?.

Answer 1

a = 9 m ( edge of a lower base ) ; b = ?; H = 8 m
V = H/3 * ( B 1 + √B 1 B 2 + B 2 )
135 = 8/3 ( 9²√3 / 4 + 9 b√3/4 + b²√3/4 )
135 = 2/3 ( 81√3 + 9 b√3 + b²√3 )
135√3 / 2 = 81 + 9 b + b²
b² + 9 b + 81 = 117
b² + 9 b - 36 = 0
b 1/2 = (- 9 + √(81 + 144 )) / 2
b = (- 9 + 15)/ 2
b = 3 m
The upper base edge is 3m long.