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
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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this one please
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56df9dae-fefa-42d0-9d05-38b84ce2f9c0%2F9b0743bc-f6b2-48ef-8330-a8ba0d955fbf%2Fsu5ks6w_processed.jpeg&w=3840&q=75)
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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