A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 4 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 16000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. The radius of the cylindrical base (and of the hemisphere) is ____ (Round to the nearest tenth as needed.) The height ___
Added by Irene S.
Step 1
Step 1: Let's denote the radius of the cylindrical base (and of the hemisphere) as r and the height of the cylinder as h. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Megan Banks and 73 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Sri K.
A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 4 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 4000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. Determine the radius and the height.
Shyam P.
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere (see the accompanying figure). If the silo is to have a capacity of $504 \pi \mathrm{ft}^{3}$, find the radius and height of the silo that requires the least amount of material to construct. Hint: The volume of the silo is $\pi r^{2} h+\frac{2}{3} \pi r^{3},$ and the surface area (including the floor) is $\pi\left(3 r^{2}+2 r h\right)$
Applications of the Derivatives
Optimization II
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD