Question

helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. which is the slant height of the pyramid if helen uses all the clay? 3 inches 4 inches 5 inches 6 inches

Explanation:

1. First, find the height of the pyramid using the volume formula:

• The volume formula for a square - based pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the height of the pyramid.
• The area of the square base with side length \(s = 6\) inches is \(B=s^{2}=6^{2}=36\) square inches.
• We know that \(V = 48\) cubic inches. Substituting into the volume formula \(48=\frac{1}{3}\times36\times h\).
• Simplify the right - hand side: \(\frac{1}{3}\times36\times h = 12h\).
• Then, solve for \(h\): \(12h=48\), so \(h = 4\) inches.

1. Then, find the slant height \(l\) using the Pythagorean theorem:

• For a square - based pyramid, if the base edge is \(s\) and the height is \(h\), the relationship between the height \(h\), half of the base edge \(\frac{s}{2}\), and the slant height \(l\) is given by the Pythagorean theorem \(l=\sqrt{h^{2}+(\frac{s}{2})^{2}}\).
• Here, \(s = 6\) inches, so \(\frac{s}{2}=3\) inches and \(h = 4\) inches.
• Substitute into the formula: \(l=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\) inches.

Answer:

C. 5 inches