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The slant height of the pyramid will be 5 inches.
Given Information and Formula Used
Volume of the clay = 48 cubic inches
Edge of the square base of the pyramid, a= 6 inches
Volume of the pyramid = (1/3) × Base Area × Height
Pythagoras Theorem, l² = x² + h²
Here, l is the hypotenuse, x is the base and [tex]h[/tex] is the height in a right angle triangle.
Calculating the Height, h of the Pyramid
Volume of the pyramid = Volume of the clay
Volume of the pyramid, V= 48 cubic inches
Base Area of the pyramid, B = a²
⇒ B = 6² square inches
⇒ B = 36 square inches
∵ V = (1/3)×B×H
[tex]\frac{1}{3}*36*h = 48[/tex]
∴ [tex]h = \frac{48*3}{36}[/tex]
⇒ h = 4 inches
Calculating the Slant Height, l of the Pyramid
Applying Pythagoras Theorem to determine the slant height,
l² = x² + h²
Here, we have x=a/2
[tex]l^{2} = \frac{a^{2} }{4} + b^{2}[/tex]
[tex]l^{2} = \frac{6^{2} }{4} + 4^{2}[/tex]
[tex]l = \sqrt{9+16}[/tex]
[tex]l=\sqrt{25}[/tex]
l =5 inches
Thus, the slant height of the solid right pyramid with a square base made by Helen is 5 inches.
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