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