we know that
The volume of the pyramid is equal to
\(V=\frac{1}{3} B*h\)
where B is the area of the base
h is the height of the pyramid
Step \(1\)
Find the height of the pyramid
we know that
the base is a square
so
\(B=6^{2} =36\ in^{2}\)
\(V=48\ in^{3}\)
\(V=\frac{1}{3} B*h\\ \\ h=\frac{3*V}{B} \\ \\ h=\frac{3*48}{36} \\ \\ h=4\ in\)
Step \(2\)
Find the slant height of the pyramid
we know that
Applying the Pythagorean Theorem
\(l^{2} =h^{2} +\frac{b}{2} ^{2}\)
where
l is the slant height
h is the height of the pyramid
b is a base edge of the pyramid
Substitute
\(l^{2} =4^{2} +\frac{6}{2} ^{2}\)
\(l^{2} =4^{2} +3^{2}\)
\(l =5\ in\)
therefore
the answer is the option
C. 5 inches
