Answer:
9.22 meters
Step-by-step explanation:
The formula for a pyramid is (base * height) / 3. Therefore, because it's a square, the base is 16, and thus the height divided by 3 = 3. 3 * 3 = 9, so the height is 9. Now we have a right triangle.
If the base edge = 4, half of the base edge is 2. Applying the Pythagorean Theorem, 2^2 + 9^2 = x^2 so then 4 + 81 = x^2. The square root of 85 is approximately 9.22 meters.
Answer:
9.22 m (nearest hundredth)
Step-by-step explanation:
Volume of a right square pyramid
[tex]\sf V=\dfrac{1}{3}a^2h\quad \textsf{(where a is the base edge and h is the perpendicular height)}[/tex]
Given:
Substituting the given values into the formula to find h:
[tex]\sf \implies 48=\dfrac{1}{3}(4)^2h[/tex]
[tex]\implies \sf h=9[/tex]
The relationship between the slant height, perpendicular height, and the base edge is given by using Pythagoras' Theorem, where the slant height is the hypotenuse of a right triangle.
[tex]\implies \sf h^2+\left(\dfrac{a}{2}\right)^2=l^2[/tex]
(where l is the slant height, a is the base edge and h is the perpendicular height)
[tex]\sf \implies l=\sqrt{h^2+\left(\dfrac{a}{2}\right)^2}[/tex]
Given:
Substituting the given values into the formula to find l:
[tex]\sf \implies l=\sqrt{9^2+\left(\dfrac{4}{2}\right)^2}[/tex]
[tex]\sf \implies l=\sqrt{85}[/tex]
[tex]\sf \implies l=9.22\:m\:(nearest\:hundredth)[/tex]
