Question

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 =________ cm
Width =_________ cm
Height =_________cm

Answer 1

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