Answer to Question #148816 in Geometry for anlp

Question

A regular square pyramid has an altitude of 12 m and volume of 196 m3. Determine the slant height of the pyramid.

Answer 1

Altitude, h = 12m

Volume, V = 196m³

V = a²*(h/3)

Where a = base edge

a² = V/(h/3)

a² = 3V/h

a² = (3*196)/12

a² = 49

a = 7m

The altitude divides the base edge into 2, forming a right angle triangle.

Therefore a' = 3.5m

Taking one of the triangles:

l² = (a')² + h²

where l = slant height

l² = (3.5)² + 12²

l² = 156.25

l = 12.5m