Question #148924
2. A regular square pyramid has an altitude of 12 m and volume of 196 m3. Determine the slant height of the pyramid.
1
Expert's answer
2020-12-08T10:18:13-0500

Consider a regular square pyramid

Let a=a= the base edge, h=h= the altitude, and s=s= the slant height.

The volume VV of the frustum of a regular square pyramid is


V=13a2hV=\dfrac{1}{3}a^2h

Then

a=3Vh=3(196)12=7(m)a=\sqrt{\dfrac{3V}{h}}=\sqrt{\dfrac{3(196)}{12}}=7 (m)

By the Pythagorean Theorem from the right triangle


s2=(a2)2+h2s^2=(\dfrac{a}{2})^2+h^2

s=(a2)2+h2=(72)2+(12)2=12.5(m)s=\sqrt{(\dfrac{a}{2})^2+h^2}=\sqrt{(\dfrac{7}{2})^2+(12)^2}=12.5(m)

12.5 m



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