+140 A solid block of soapstone is used to carve a perfect rectangular prism. It has dimensions 12cm long, 10cm wide and 6cm in height. The carver wants to reduce the volume of the block by 400cm3 by removing the same amount off all three dimensions. Write a polynomial equation that represents the volume of the block. Calculate algebraically how much he should remove from each dimension.
i am completely stumped on how to do this and/or similar equations
+33661 Assume x cm taken off each side.
Reduced volume = (12 - x)(10 - x)(6 - x) cm3
= (120 - 22x + x2)(6 - x)
= 720 - 252x + 28x2 - x3
This must equal 12*10*6 - 400 = 720 - 400cm3
720 - 400 = 720 - 252x + 28x2 - x3
x3 - 28x2 + 252x - 400 = 0
Real number solution: x = 2 cm
i.e. 2 cm must be removed from each side.
