Answer:
the cylinder container has the greatest surface area.
Step-by-step explanation:
The volume of cone is calculated by [tex]v=\frac{1}{3}\times\pi\times r^{2}\times h[/tex]
The volume of cylinder is calculated by [tex]v=\pi\times r^{2}\times h[/tex]
The volume of square pyramid is calculated by [tex]v=\pi\times r^{2}\times h[/tex]
The volume of rectangular prism is calculated by [tex]v=\frac{1}{3}\times B\times h[/tex]
The radius of cone is [tex]\frac{6}{3}[/tex]=[tex]2in[/tex], and slant height is 10 in.
height is calculated as h² = l²- r²
h² = l²- r²
h² = 10²- 3²
h² = 100- 9
h² =91
h= 9.54
The volume of cone is [tex]=\frac{1}{3}\times 3.14\times 3^{2}\times 9.54[/tex]
[tex]=\frac{1}{3}\times 3.14\times 9\times 9.54[/tex]
v=89.8668
The volume of cylinder is [tex]=3.14\times 3^{2}\times 10[/tex]
[tex]=3.14\times9\times 10[/tex]
v=282.6
The volume of square pyramid
The height of pyramid is calculated as h² = l²- r²
h² = 10²- 3²
h² = 100- 9
h² =91
h= 9.54
[tex]v=3.14\times 3^{2}\times 9.54[/tex]
[tex]v=3.14\times 9\times 9.54[/tex]
[tex]v=269.60[/tex]
The volume of rectangular prism[tex]v=\frac{1}{3}\times 6\times 10[/tex]
[tex]v=20[/tex]
Hence, the cylinder container has the greatest surface area.
