Question

what is the volume of a square Peerman with the base edges of 40 cm and a slant height of 25 cm

533.3 cm^3
8,000 cm^3
12,000 cm^3
24,000 cm^3

Answer 1

\[V= \frac{ 1 }{ 3 }b ^{2}h\]This equation is just for a square pyramid and uses height (altitude). In this problem you were given the slant height (length of hypotenuse). To calculate the height use the pythagorean theorem\[a ^{2} + b ^{2} = c ^{2}\]

c in this case = 25cm. a = half of 40 which is 20cm. So it can be written as

20^2 + h^2 = 25^2

400 + h^2 = 625

minus 400 from both sides

h^2 = 225

take the square root from both sides

h = 15

Now calculate

\[\frac{ 40^{2}15 }{ 3 }\]