You have a wire that is 86 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum? The circumference of the circle is cm. Give your answer to two decimal places

You have a wire that is 86 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum? The circumference of the circle is cm. Give your answer to two decimal places

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter64: Volumes Of Spheres And Composite Solid Figures

Section: Chapter Questions

Problem 1A: In order to make a conical duct a circular sheet of metal is to be cut in the shape of a sector of a...

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.
The volume V of a cone with height h and diameter d is given by V=0.2618d2h . What is the volume of a cone with diameter 72.4 cm and height 122.5 cm? Round the answer to 2 decimal places.
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)?
The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
The roof of the house shown needs to be reshingled. a Considering that the front and back sections of the roof have equal areas, find the total area to be reshingled. b If roofing is sold in squares each covering 100ft2, how many squares are needed to complete the work? c To remove old shingles and replace with new shingles costs 97.50 per square. What is the cost of reroofing?
A slot is machined in a circular plate with a 41.36-millimeter diameter. Two milling cuts, one 6.30 millimeters deep and the other 3.15 millimeters, are made. A grinding operation then removes 0.40 millimeter. What is the distance from the center of the plate to the bottom of the slot? All dimensions are in millimeters.
Find the area of a triangle with sides that are 418 in., and 612 in. long. Round your answer to 2 decimal places.
In order to make a conical duct a circular sheet of metal is to be cut in the shape of a sector of a circle. It the radius of the sector is 32.5 in. and the arc length of the sector is 264 in., what will be the volume of the cone? Round the answer to 1 decimal place.
A square bar 78 in. on a side is to be milled from a circular rod. If the available rods are 1 in., 114 in, and 112 in. and 2 in. in diameter, which rod should be used so there is the least waste? How much waste, in area, will there be with the selected rod? Round your answer to 2 decimal places.
For a right circular cone, the slant height has a measure equal to twice that of the radius length of the base. If the total area of the cone is 48in2, what are the dimensions of the cone?