OPTIMIZING SHAPES:

can someone please help me with these questions i'm really confused

I'm suppose to figure out the dimensions of prism with the volume that is provided.

And use the optimization formula that is provided.

Optimization Formulas The following What you are Desired Shape equations will be given useful: With 4 sides of fencing Perimeter P = 4w or A = Ixw or A = w2 Maximizing a Area rectangular area given its perimeter With 3 sides of Fencing or Perimeter P = 4w Minimizing a or A= Ixw or A= 2w2 rectangular Area 2w perimeter given its area With 2 sides of fencing Perimeter P = 2w N or A = Ixw or A=w2 Area W Minimizing the surface area of a Volume V = $3 square-based prism or Maximizing the volume of a Surface Area SA = 6s2 square-based prism S h = d orh = 2r Substituting h = 2r into SA = 2nr2 + 2rrh, we get SA = 2nr2 + 2nr(2r) Maximizing the Surface Area SA = 2nr2 + 4mr2 volume of a 2r SA = 6ntr2 cylinder or h = dor h = 2r Substituting h = 2r into Minimizing the V = nr 2h, we get surface area of a V = nr 2(2r) cylinder Volume V = 2mr3 2Cylinder Abase = 100 h = ? h = V \\Abase H = 400/ 100 = 4 Abase = Pix r2 =100 3.1416x r2 = 100 r2=100/3.1416=31.831 r=5.60m Check: V = Pi x r2 x hprism=3f|416x5.62x4=394.1cm3 PART 2 OF THE ASSIGNMENT Volume = x3 Solve for x. Surface Area = 6x2 example: V = 400 400 = x3 W = x X = 7.4 S.A. = 6(7.4)2 S.A. = 326 minimum PART 1 OF THE ASSIGNMENT Figuring out dimensions of prisms with given volume Vprism = Area base X heightprism V = 400cm3 rectangular prism Abase = 100cm2 hprism = ? hprism = VI Abase hprism = 400 / 100 = 4cm Abase = W X 1 =100cm2 W = 25 1 = 4 or W = 10 1 = 10 W=5 1=20 Dimensions of rectangular prism 25cm by 4cm by 4cm L W h Check: V = w x | x h = 25x4x4=400cm3 Right Isosceles Triangular prism 90 two sides are equal Abase = 100cm3 hprism = ? hprism = V \\ Abase hprism = 400 / 100 = 4cm a = b=h Abase = (b x h)/2 =(a x a)/2=100cm2 axa = a2 = 200cm2 a = 14cm b=14cm hbase=14cm hprism=4cm Check: V=[(14.14x14.14)/2]x4=400cm3