Question

Claire built two similar wooden chests in the shape of rectangular prisms. She needed 6 pints of paint to cover the outside of the larger chest fully and 4 pints to cover the outside of the smaller chest. How much more volume does the larger chest contain?
A.
122% more
B.
150% more
C.
184% more
D.
338% more

Answer 1

 The amount of paint has to do with surface area, which is the 'scale factor' squared. 
The ratio of the volumes is the 'scale factor' cubed. 

(The term scale factor is the ratio of a pair of corresponding sides of the similar figures). 

(Scale factor)² = 6/4 = 3/2 
Scale factor = √3 / √2 

Volume ratio = (√3 / √2)³ = 3√3 / 2√2 

SInce 3√3 / 2√2 = 1.837, this implies the larger chest is 83.7% larger in volume than the smaller (i.e., "184% of the smaller")