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 8101 in³.

The suitcase has a volume of about 10,368 in³, or about 1105 in³.

11058101=18104, 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 8102.

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.

Question

Mathematics

Camryn Shepard

3 August, 13:01

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 8101 in³.

The suitcase has a volume of about 10,368 in³, or about 1105 in³.

11058101=18104, 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 8102.

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.

+3

Answers (1)

Know the Answer?

Diana Frank · 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.