4 [It is given that a sphere of radius r has volume 3 cm r cm Handle Cover Disc cm Body h cm 1 cm r cm 1 cm 1 cm Front view of container Cross-section of body A container is made up of 2 parts. A cylindrical body, opened at one end, of external radius r cm (where r> 1), external height h cm and thickness 1 cm throughout. A cover consisting of a solid cylindrical disc with radius r cm and height 1 cm and a hemispherical handle with radius one-third of the radius of the disc. The internal volume of the cylindrical body is 30 cm³ when full. The material used to make the body and the cover of the container costs $0.50 per cm'. (i) Find an expression for h in terms of r. (ii) Show that the cost, $ C , to make the container is given by C =Tr'+ 81 15r? +ar² -15. (r-1) (iii) Given that r =r, is the value of r which gives the stationary value of C, show tnat n satisfies the equation 27 30r +2ar 0. Hence find the values of r and A (r-1) which give the minimum value of C. [(i) h =- 30 +1, (iii) r = 2.66, h = 4.48] T (r-1)
4 [It is given that a sphere of radius r has volume 3 cm r cm Handle Cover Disc cm Body h cm 1 cm r cm 1 cm 1 cm Front view of container Cross-section of body A container is made up of 2 parts. A cylindrical body, opened at one end, of external radius r cm (where r> 1), external height h cm and thickness 1 cm throughout. A cover consisting of a solid cylindrical disc with radius r cm and height 1 cm and a hemispherical handle with radius one-third of the radius of the disc. The internal volume of the cylindrical body is 30 cm³ when full. The material used to make the body and the cover of the container costs $0.50 per cm'. (i) Find an expression for h in terms of r. (ii) Show that the cost, $ C , to make the container is given by C =Tr'+ 81 15r? +ar² -15. (r-1) (iii) Given that r =r, is the value of r which gives the stationary value of C, show tnat n satisfies the equation 27 30r +2ar 0. Hence find the values of r and A (r-1) which give the minimum value of C. [(i) h =- 30 +1, (iii) r = 2.66, h = 4.48] T (r-1)
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
Section9.1: Prisms, Area And Volume
Problem 30E: A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases....
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![4
[It is given that a sphere of radius r has volume
3
cm
r cm
Handle
Cover
Disc
cm
Body
h cm
t1 cm
r cm
1 cm
1 cm
Front view of container
Cross-section of body
A container is made up of 2 parts.
A cylindrical body, opened at one end, of external radius r cm (where r> 1), external
height h cm and thickness 1 cm throughout.
A cover consisting of a solid cylindrical disc with radius r cm and height 1 cm and a
hemispherical handle with radius one-third of the radius of the disc.
The internal volume of the cylindrical body is 30 cm³ when full. The material used
to make the body and the cover of the container costs $0.50 per cm³.
(i)
Find an expression for h in terms of r.
(ii) Show that the cost, $ C , to make the container is given by
15r?
+ar² -15.
(r-1)
1
C =
nr +
81
(iii) Given that r = r, is the value of r which gives the stationary value of C, show tnat
n satisfies the equation
27
30r
+2ar = 0. Hence find the values of r and h
(r-1)
which give the minimum value of C.
30
+1, (iii) r = 2.66, h= 4.48]
[(i) h=-
7(r-1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F902f5c45-8106-4c05-84fa-6818a38e7876%2F81904fef-8d0e-419c-ab0d-7457881ea1f7%2F8gqgqca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4
[It is given that a sphere of radius r has volume
3
cm
r cm
Handle
Cover
Disc
cm
Body
h cm
t1 cm
r cm
1 cm
1 cm
Front view of container
Cross-section of body
A container is made up of 2 parts.
A cylindrical body, opened at one end, of external radius r cm (where r> 1), external
height h cm and thickness 1 cm throughout.
A cover consisting of a solid cylindrical disc with radius r cm and height 1 cm and a
hemispherical handle with radius one-third of the radius of the disc.
The internal volume of the cylindrical body is 30 cm³ when full. The material used
to make the body and the cover of the container costs $0.50 per cm³.
(i)
Find an expression for h in terms of r.
(ii) Show that the cost, $ C , to make the container is given by
15r?
+ar² -15.
(r-1)
1
C =
nr +
81
(iii) Given that r = r, is the value of r which gives the stationary value of C, show tnat
n satisfies the equation
27
30r
+2ar = 0. Hence find the values of r and h
(r-1)
which give the minimum value of C.
30
+1, (iii) r = 2.66, h= 4.48]
[(i) h=-
7(r-1)
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