Question

Calculate the volume of a square pyramid if it has a base area of 64 cm^2 and the distance from the apex to a corner of the base is 15 cm.

Thank you so much!!!

Answer 1

Base length = a = sqrt64 = 8 cm
Distance from corner to center of base
= a*sqrt2 = 11.314 cm
Pyramid height =
h = sqrt[15^2 -(8sqrt2)^2]
= sqrt[225 - 128]= 9.85 cm

Volume = (base area)*(height)/3
= 210 cm^3

Answer 2

Side of base = √64 = 8 cm

Distance from centre to corner of base
=8(√2)/2=4√2

Let h=height,
h²=15²-(4√2)²
=225-32=193
h=√193 = 13.89 cm approx.

Volume
=(64)h/3
=64*(√193)/3
=296.4 cm³ approx.