A rectangular prism has a volume of 16 cm3 and a total surface area of 40 cm2. A similar prism has length 10 in., width 5 in., and height 5 in. What are the dimensions of the original prism? Enter your answers in the boxes.Length =________ cmWidth =_________ cmHeight =_________cm
Accepted Solution
A:
we know that [volume of the similar prism]=10*5*5----> 250 in³ volume original prism=16 cm³ 1 in³---------> 16.3871 cm³ X----------> 16 x=16/16.3871------> x=0.9764 in³
[volume of the similar prism]=[scale factor]³*[volume original prism] [scale factor]³=[volume of the similar prism]/[volume original prism] [scale factor]³=[250]/[0.9764]------> 256.05 scale factor=∛256.05-------> 6.35
the dimensions of the original prism are 1 in-----> 2.54 cm
length 10 in/6.35-------> 1.57 in*2.54 cm/in-----> 4 cm width 5 in/6.35---------> 0.79 in*2.54 cm/in-----> 2 cm height 5 in/6.35--------> 0.79 in*2.54 cm/in----> 2 cm