Answer:
option c is correct
slant height of the pyramid is, 5 inches
Step-by-step explanation:
Volume of a pyramid(V) is given by:
[tex]V = \frac{1}{3} \cdot B \cdot h[/tex]
where,
B is the base area
h is the height.
As per the statement:
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.
Since, base is square
⇒Base area = [tex](side)^2[/tex]
⇒ Base area = [tex]6^2 = 36[/tex] square inches.
and
volume of solid square right pyramid(V)= 48 cubic inches
Substitute these we have;
[tex]48 = \frac{1}{3} \cdot 36 \cdot h[/tex]
⇒[tex]48 = 12h[/tex]
Divide both sides by 12 we have;
[tex]h = 4[/tex] inches.
To find the slant height:
Using Pythagoras theorem.
[tex]l^2 = h^2+\frac{b^2}{4}[/tex]
where
l is the slant height
b is the base edge of the pyramid.
then;
[tex]l^2 = 4^2+\frac{36}{4}[/tex]
⇒[tex]l^2 = 16+9 = 25[/tex]
⇒[tex]l = \sqrt{25} =5[/tex] inches
therefore, the slant height of the pyramid is, 5 inches
