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:
\(V = \frac{1}{3} \cdot B \cdot h\)
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 = \((side)^2\)
⇒ Base area = \(6^2 = 36\) square inches.
and
volume of solid square right pyramid(V)= 48 cubic inches
Substitute these we have;
\(48 = \frac{1}{3} \cdot 36 \cdot h\)
⇒\(48 = 12h\)
Divide both sides by 12 we have;
\(h = 4\) inches.
To find the slant height:
Using Pythagoras theorem.
\(l^2 = h^2+\frac{b^2}{4}\)
where
l is the slant height
b is the base edge of the pyramid.
then;
\(l^2 = 4^2+\frac{36}{4}\)
⇒\(l^2 = 16+9 = 25\)
⇒\(l = \sqrt{25} =5\) inches
therefore, the slant height of the pyramid is, 5 inches
