Question

Dana is holding a bottle of shampoo, which is cylindrical in shape with a radius of about 2 in. and a height of about 7 in. She is wondering how many bottles of this shampoo she can fit in a suitcase that is shaped like a rectangular prism and is about 3 ft long, 2 ft wide, and 1 ft tall. Her reasoning, shown here, contains an error.
The shampoo bottle has a volume of about 88 in³, or about 8×101 in³.
The suitcase has a volume of about 10,368 in³, or about 1×105 in³.
1×1058×101=18×104 , so about 1250 bottles of shampoo could fit in the suitcase.

What is Dana's error?

A. The value 88 should have been rounded to 8×102 .
B. The volume of the shampoo bottle is not 88 in³.
C. The volume of the suitcase is not about 10,368 in³.
D. The value 10,368 should have been rounded to 1×104 .

Answer 1

Volume of the shampoo bottle
                                    V = πr²h
Substituting,
                                      V = π(2 in)²(7 in) = 87.9 in³  ≈ 88 in³

Volume of the suitcase,
         Convert all dimensions to inches by multiplying by 12.
                              length = 36 in  ;  width = 24 in   ; height = 12 in

Multiply the given dimensions,
                                  V = (36 in)(24 in)(12 in) = 10,368 in³

Dividing the two calculated values will give us an answer of 117.82 or approximately 117 bottles. 

The mistake done is described in letter A because as much as possible we want to overestimate the volume of the shampoo as its value becomes the divisor.