Let PQRSTUVW be a rectangular prism, as shown. The area of face PQRS is 6. The area of face PQUT is 15. The area of face QUVR is 10. Find the volume of the rectangular prism.
+128407 Area of base = QP * QR = 6 (1)
Area of one side POUT = QP * QU = 15 ⇒ QP = 15/QU (2)
Area of the other side QUVR = QU * QR = 10 ⇒ QR = 10/QU (3)
Sub (2) , (3) into (1)
15/ QU * 10/QU = 6
150 / QU^2 = 6 rearrange as
QU^2 = 150/6
QU^2 = 25 take the square root
QU = 5
So QP = 15/5 = 3
And QR = 10/5 = 2
So....the volume is QU * QP * QR = 5 * 3 * 2 = 30 units^3
