Question

Which container has the greatest surface area? (Use 3.14 for π .)

Answer 1

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

$SA=\pi r^{2} +\pi rl$

we have

$r=6/2=3\ in$ ----> the radius is half the diameter

$l=10\ in$

substitute the values

$SA=(3.14)(3)^{2} +(3.14)(3)(10)=122.46\ in^{2}$

case B) A cylinder

The surface area of a cylinder is equal to

$SA=2\pi r^{2} +2\pi rh$

we have

$r=6/2=3\ in$ ----> the radius is half the diameter

$h=10\ in$

substitute the values

$SA=2(3.14)(3)^{2} +2(3.14)(3)(10)=244.92\ in^{2}$

case C) A square pyramid

The surface area of a square pyramid is equal to

$SA=b^{2} +4[\frac{1}{2}bh]$

we have

$b=6\ in$ ----> the length side of the square

$h=10\ in$ ----> the height of the triangular face

substitute the values

$SA=6^{2} +4[\frac{1}{2}(6)(10)]=156\ in^{2}$

case D) A rectangular prism

The surface area of a rectangular prism is equal to

$SA=2b^{2} +4[bh]$

we have

$b=6\ in$ ----> the length side of the square base

$h=10\ in$ ----> the height of the rectangular face

substitute the values

$SA=2(6)^{2} +4[(6)(10)]=312\ in^{2}$