Refer back to the Learning Activity titled “Applications of Volume and Surface Area.” Problem 2 introduces a company that is trying to decide whether to manufacture cube-shaped or sphere-shaped tree ornaments. In your own words, explain what calculations were made, and why, in solving this problem. Why would a company be doing those calculations in the first place? If possible, give an example of a similar situation within your common experience in which the type of packaging shape is a variable for company decision-making.
Refer back to the Learning Activity titled “Applications of Volume and Surface Area.” Problem 2 introduces a company that is trying to decide whether to manufacture cube-shaped or sphere-shaped tree ornaments. In your own words, explain what calculations were made, and why, in solving this problem. Why would a company be doing those calculations in the first place? If possible, give an example of a similar situation within your common experience in which the type of packaging shape is a variable for company decision-making.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Applying Geometry
Refer back to the Learning Activity titled “Applications of Volume and Surface Area.” Problem 2 introduces a company that is trying to decide whether to manufacture cube-shaped or sphere-shaped tree ornaments. In your own words, explain what calculations were made, and why, in solving this problem. Why would a company be doing those calculations in the first place? If possible, give an example of a similar situation within your common experience in which the type of packaging shape is a variable for company decision-making.
Transcribed Image Text:Problem 2
A company is trying to decide between a spherical-or cube-shaped tree ornament. Which ornament would require
less paint?
A spherical ornament with a diameter of 2.48 inches
A cube-shaped ornament with a side length of 1.80 inches
Step 1. Sketch a diagram and label with the appropriate measurements. What are the relevant formulas we might use
for this problem?
Explanation:
The relevant formulas for a sphere are:
SA = 4rr2
V = (4/3)πr3
The relevant formulas for a cube are:
SA = 6s2
V = $3
Because the ornaments are being painted, we are concerned with surface area for each.
Step 2. Identify all the known values you can substitute into the surface area formula.
Sphere ornament:
SA =
r =
Cube ornament:
SA =
S =
Explanation:
Sphere ornament:
SA=unknown
r = 1.24 inches
Cube ornament:
SA = unknown
S = 1.8 inches
Step 3. Substitute into the surface area formula for both spheres.
Sphere ornament:
Cube ornament:
Explanation:
Sphere ornament: SA = 4(1.24)2 = 19 square inches
Cube ornament: SA = 6 (1.8)2 = 19 square inches
Step 4. Use your calculations to answer the original question.
Answer: The surface area is equivalent so the cost of paint for either will be the same. The company could go with
either shape of ornament.
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
