A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the what should the radius of the base of the cup be material for the sides costs 29¢/in.2 and the material for the base costs 46c/in. to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable r for the quantity to be optimized. f(r) = ( cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of ---Select- . (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=

A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular cylinder with an open top. If the what should the radius of the base of the cup be material for the sides costs 29¢/in.2 and the material for the base costs 46c/in. to minimize the construction cost (in ¢)? Letr and h (in in.) be the radius and height of the pencil cup, respectively. in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable r for the quantity to be optimized. f(r) = ( cents (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of r. h = (d) To determine the optimal value of the function f, we need the critical numbers of ---Select- . (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) r=

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.4: Polyhedrons And Spheres

Problem 24E: A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of...

See similar textbooks

Similar questions

The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
A calendar is determined by using each of the 12 faces of a regular dodecahedron for one month of the year. With each side of the regular pentagonal face measuring 4cm, the area of each face is approximately 27.5 cm2. a What is the total surface area of the calendar? b If the material used to construct the calendar costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
Cycling The Campagnolo Hyperon Ultra Two carbon wheel, which has a diameter of 700 millimeters, has 22 spokes evenly distributed around the rim of the wheel. What is the length of the rim subtended by adjacent pairs of spokes (Figure 15)?
A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases. With dimensions as shown, what is the storage capacity volume of its interior?
Compute the number of cubic centimeters of material in the locating saddle shown. Round the answer to the nearest cubic centimeter.
For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is doubled while the height is made half as large in forming a new cone, will the volumes of the two cones be equal?
A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral surface 3 in. high. If the cost of the metal used is 0.5 per square inch and the cost of the cardboard is 0.2 cent per square inch, what is the approximate cost of constructing one container? Use 3.14.