A right prism has square bases with edges that are three times as long as the lateral edges. The prism's total surface area is 750 m². Find the volume.
Answer (2)
a = 3 h an d A = 2 ⋅ a 2 + 4 ⋅ a ⋅ h A = 2 ⋅ ( 3 h ) 3 + 4 ⋅ 3 h ⋅ h = 2 ⋅ 9 h 2 + 12 h 2 = 30 h 2 A = 750 m 2 ⇒ 30 h 2 = 750 / : 30 ⇒ h 2 = 25 ⇒ h = 5 ⇒ a = 15 V = a 2 ⋅ h = 1 5 2 ⋅ 5 = 225 ⋅ 5 = 1125 A n s . V o l u m e = 1125 m 3 .
The volume of the right prism with square bases is 1125 m³. This is calculated using the prism's height and the relationship between the height and the side length of the base. The total surface area provided helped determine the height, which led to finding the volume.
;
