Question 1180777


A square pyramid has a slant height of 25 m and a lateral area of 350^2 m. Which is the closest to the volume?

given:
{{{SA=350m^2}}}
a slant height {{{s=25m}}}

The {{{350m^2}}} of lateral surface area is four congruent triangles, each with height {{{25m}}}. If the side length of the square base is {{{a}}}, then

{{{4(a/2)*s=350}}}
{{{2a*25=350}}}
{{{a*50=350}}}
{{{a=350/50}}}
{{{a=7m}}}

The side length of the square base is {{{7m}}}.


The volume of a square pyramid is:

{{{V = (1/3)a^2*h}}}

{{{h=sqrt(25^2-(7/2)^2)}}}

{{{h=sqrt(2451/4)}}}

{{{h=24.75}}}


{{{V = (1/3)(7m)^2*24.75m}}}

{{{V = 404.25m^3}}}