helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches…

Explanation:

Step1: Find the base - area of the square - based pyramid

The base of the pyramid is a square with edge length (a = 6) inches. The area of the base (B=a^{2}), so (B = 6^{2}=36) square inches.

Step2: Find the height of the pyramid using the volume formula

The volume formula for a pyramid is (V=\frac{1}{3}Bh), where (V = 48) cubic inches and (B = 36) square inches. We can solve for (h): [48=\frac{1}{3}\times36\times h] [48 = 12h] [h = 4] inches.

Step3: Find the slant height of the pyramid

The base edge is (a = 6) inches, so the distance from the center of the base to an edge is (\frac{a}{2}=3) inches. Using the Pythagorean theorem in the right - triangle formed by the height of the pyramid ((h = 4) inches) and half of the base edge length ((3) inches) to find the slant height (l). [l=\sqrt{h^{2}+\left(\frac{a}{2}\right)^{2}}] [l=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5] inches.

Answer:

5 inches