The legs of an elephant are much thicker in proportion to its body than the legs of a mouse. This is due to the "square-cube" law. The mass of an animal is (roughly) proportional to the cube of its height, while the strength of a limb is proportional to the square or the animal's height. So if an animal doubles in height, its mass will be 8 times greater than it was, but its strength will only be 4 times greater than it was, assuming the limbs maintain their original proportions. This can be represented using 2 the relations = where s is the strength factor (or thickness factor) required for the limbs, 1 is the original height, and h is the new height. Both k1 and h, are measured in units of length, so the ratio is a number without any units, as is s. a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla from which it is modelled. To comply with the square-cube law, how much thicker must the legs be, compared with the gorilla's? b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several small lizards that are alive today and that grow to a height of about 50 cm. Predict how the relative thickness of the brachiosaur's legs compares with the thickness of the lizard's legs.
The legs of an elephant are much thicker in proportion to its body than the legs of a mouse. This is due to the "square-cube" law. The mass of an animal is (roughly) proportional to the cube of its height, while the strength of a limb is proportional to the square or the animal's height. So if an animal doubles in height, its mass will be 8 times greater than it was, but its strength will only be 4 times greater than it was, assuming the limbs maintain their original proportions. This can be represented using 2 the relations = where s is the strength factor (or thickness factor) required for the limbs, 1 is the original height, and h is the new height. Both k1 and h, are measured in units of length, so the ratio is a number without any units, as is s. a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla from which it is modelled. To comply with the square-cube law, how much thicker must the legs be, compared with the gorilla's? b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several small lizards that are alive today and that grow to a height of about 50 cm. Predict how the relative thickness of the brachiosaur's legs compares with the thickness of the lizard's legs.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question

Transcribed Image Text:The legs of an elephant are much thicker in proportion to its body than the legs of a
mouse. This is due to the "square-cube" law. The mass of an animal is (roughly)
proportional to the cube of its height, while the strength of a limb is proportional to
the square or the animal's height. So if an animal doubles in height, its mass will be 8
times greater than it was, but its strength will only be 4 times greater than it was,
assuming the limbs maintain their original proportions. This can be represented using
(A)
the relation s =
where s is the strength factor (or thickness factor) required for
the limbs, k1 is the original height, and h is the new height. Both k1 and are
measured in units of length, so the ratio is a number without any units, as is s.
a) A giant ape in a science fiction movie has 10 times the height of the 2 m tall gorilla
from which it is modelled. To comply with the square-cube law, how much thicker
must the legs be, compared with the gorilla's?
b) A brachiosaur was typically 15.2 m in height. Its build resembled that of several
small lizards that are alive today and that grow to a height of about 50 cm. Predict
how the relative thickness of the brachiosaur's legs compares with the thickness of
the lizard's legs.
M|N
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images

Recommended textbooks for you

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON

Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON

Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning

Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON

Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press

College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education