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9 Abox is made from an 80 cm by 30 cm rectangle of cardboard by cutting out 4 equal squares of side x cm from each corner. The edges are turned up to make an open box. Show that the volume of the box is given by the equation V = 4x' – 220x² + 2400x. b Find the value of x that gives the box its greatest volume. 80 cm %3D Find the maximum volume of the box. 30 cm

9 Abox is made from an 80 cm by 30 cm rectangle of cardboard by cutting out 4 equal squares of side x cm from each corner. The edges are turned up to make an open box. Show that the volume of the box is given by the equation V = 4x' – 220x² + 2400x. b Find the value of x that gives the box its greatest volume. 80 cm %3D Find the maximum volume of the box. 30 cm

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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9 Abox is made from an 80 cm by 30 cm rectangle of cardboard by cutting out 4 equal squares of side x cm from each corner. The edges are turned up to make an open box. 80 cm Show that the volume of the box is given by the equation V = 4x'– 220x + 2400x. Find the value of x that gives the box its greatest volume. Find the maximum volume of the box. a 10 The formula for the surface area of a cylinder is given by S= 2n(r+ h) where r is the radius of its base and h is its height. Show that if the cylinder holds a volume of 54r m’, the surface area is given by the %3D 108T equation S = 2r + r. b Hence find the radius that gives the minimum surface area. 11 A silo in the shape of a cylinder is required to hold 8600 m' of wheat. Find an equation for the surface area of the silo in terms of the base radius. b Find the minimum surface area required to hold this amount of wheat, to the nearest square metre. 30 cm
Transcribed Image Text:9 Abox is made from an 80 cm by 30 cm rectangle of cardboard by cutting out 4 equal squares of side x cm from each corner. The edges are turned up to make an open box. 80 cm Show that the volume of the box is given by the equation V = 4x'– 220x + 2400x. Find the value of x that gives the box its greatest volume. Find the maximum volume of the box. a 10 The formula for the surface area of a cylinder is given by S= 2n(r+ h) where r is the radius of its base and h is its height. Show that if the cylinder holds a volume of 54r m’, the surface area is given by the %3D 108T equation S = 2r + r. b Hence find the radius that gives the minimum surface area. 11 A silo in the shape of a cylinder is required to hold 8600 m' of wheat. Find an equation for the surface area of the silo in terms of the base radius. b Find the minimum surface area required to hold this amount of wheat, to the nearest square metre. 30 cm
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