Question

A prism has total surface area of 360 m2 and volume of 60 m3.

Answer 1

We know that

If each dimension is scaled by a factor x, then the area of each side, and thus the surface area, is scaled by x² and the volume is scaled by x³. 

Thus, 
Part a) if the length, width, and height are reduced to half their original sizes, the area of each side is scaled by a factor of 
(1/2)²------> 1/4 
and 
the volume is scaled by a factor of 
(1/2)³-----> 1/8. 

Thus, 
if the initial surface area is 360 m², 
the final surface area is (1/4)(360 m²) = 90 m².

 If the initial volume is 60 m³, 
then 
the final volume is (1/8)(60 m³) = 7.5 m³. 

Part B_ If the length, width, and height are tripled, the area of each side is scaled by a factor of 
(3)²-----> 9 
and 
the volume is scaled by a factor of 
(3)³-------> 27. 

Thus, 
if the initial surface area is 360 m², 
the final surface area is (9)(360 m^2) = 3240 m². 

If the initial volume is 60 m³, 
then
 the final volume is (27)(60 m^3) = 1620 m³.