Answer:
The rectangular prism has the greatest surface area
Step-by-step explanation:
Verify the surface area of each container
case A) A cone
The surface area of a cone is equal to
[tex]SA=\pi r^{2} +\pi rl[/tex]
we have
[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter
[tex]l=10\ in[/tex]
substitute the values
[tex]SA=(3.14)(3)^{2} +(3.14)(3)(10)=122.46\ in^{2}[/tex]
case B) A cylinder
The surface area of a cylinder is equal to
[tex]SA=2\pi r^{2} +2\pi rh[/tex]
we have
[tex]r=6/2=3\ in[/tex] ----> the radius is half the diameter
[tex]h=10\ in[/tex]
substitute the values
[tex]SA=2(3.14)(3)^{2} +2(3.14)(3)(10)=244.92\ in^{2}[/tex]
case C) A square pyramid
The surface area of a square pyramid is equal to
[tex]SA=b^{2} +4[\frac{1}{2}bh][/tex]
we have
[tex]b=6\ in[/tex] ----> the length side of the square
[tex]h=10\ in[/tex] ----> the height of the triangular face
substitute the values
[tex]SA=6^{2} +4[\frac{1}{2}(6)(10)]=156\ in^{2}[/tex]
case D) A rectangular prism
The surface area of a rectangular prism is equal to
[tex]SA=2b^{2} +4[bh][/tex]
we have
[tex]b=6\ in[/tex] ----> the length side of the square base
[tex]h=10\ in[/tex] ----> the height of the rectangular face
substitute the values
[tex]SA=2(6)^{2} +4[(6)(10)]=312\ in^{2}[/tex]
