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Q9)

You plan to build a cylindrical container with no top. The material used for the lateral sides costs $2 per square foot while the material for the bottom costs $7 per square foot.

Explanation / Answer

1.
A(c)= C^2/4pi

V(r)= 1/3* pi*r^2*8r= 8/3*pi*r^3

D(w)= w^2 + 64/w^2

2,

C= 2*2*pi*r*h + 7*pi*r^2

pi*r^2*h= 150

h= 150/(pi*r^2)

C= 4*pi*r*150/(pi*r^2) + 7*pi*r^2

3.

A(r)= 4r* 2r= 8r^2

P(r)= 2(4R+2R)= 12 r

4.

A= 0.5*x*{4th root(x)}

5.

D= sqrt((1-x)^2+ (5-x^8)^2)

6.

8/3= h/R

R= 3h/8

V= pi*r^2*h= (pi*9h^3)/64

7.

C= x^2/(4*pi)

S= x^2/16

8.

h= cot(theta)

theta= arccot(h)

9.

A= x^2+ 4*x.h

h= {A-x^2}/4x

V= x^2,h

V= x(A-x^2)/4

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