Answer: 5 inches
Step-by-step explanation:
Given: Volume of clay = 48 cubic inches
If we make a solid square right pyramid with a base edge a= 6 inches.
Then its base area = [tex]a^2=6^2=36\ inches^2[/tex]
we know that volume of square right pyramid=[tex]\frac{1}{3}\times\ a^2h[/tex]
Therefore, volume of square right pyramid made by all of clay=[tex]\frac{1}{3}\times\ a^2h[/tex]=48 cubic inches
[tex]\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}[/tex]
Now, slant height [tex]l=\sqrt{(\frac{a}{2})^2+h^2}[/tex]
[tex]\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5[/tex]
The slant height of the pyramid if Helen uses all the clay=5 inches
