Question

The pyramid in Figure 3 is composed of a square base of area $16$ and four isosceles triangles, in which each base angle measures ${60}^o$. Calculate the volume of the pyramid.

• A. $7.39$
• B. $9.24$
• C. $15.08$
• D. $21.33$
• E. $24.05$

Answer 1

Answer: (C)

$15.08$

Given, area of square base $16$ and four isosceles triangles in which base angle ${60}^o$

Then side of base of triangle $=$ $\sqrt{16}=4$

The Length from top to base of pyramid $=$ $(4{)}^2-{\left(\frac{4}{2}\right)}^2=2\sqrt{3}$

Height of pyramid $=$ $h=(2\sqrt{3}{)}^2-{\left(\frac{4}{2}\right)}^2\Rightarrow h=2\sqrt{2}$

Then, volume of pyramid $=$ $\frac{4\times 4\times 2\sqrt{2}}{3}=15.08$