Answer:
- height: 8 m
- slant height: 5 in
Step-by-step explanation:
The parameter of interest can be found by putting the given values into the appropriate volume or area formula for a pyramid, then solving for the unknown. The relevant formulas are ...
V = 1/3s²h . . . . . s is the base length; h is the height
A = s(s +2h) . . . . s is the base length; h is the slant height
__
height given volume
Using the given values for the volume and the length of the base, the formula becomes ...
V = 1/3s²h
96 m³ = 1/3(6 m)²h . . . . . . . . . . use the given values for V, s
(96 m³)/(12 m²) = 8 m = h . . . . . divide by the coefficient of h
The height of the pyramid is 8 meters.
__
slant height given area
Using the given values for area and the length of the base, the formula becomes ...
A = s(s +2h)
47.25 in² = (3.5 in)(3.5 in + 2h) . . . . use the given values for A, s
13.5 in = 3.5 in + 2h . . . . . . . . . . . divide by 3.5 in
10 in = 2h . . . . . . . . . . . . . . . . . subtract 3.5 in
5 in = h . . . . . . . . . . . . . . . . divide by 2
The slant height of the pyramid is 5 inches.
