Question

Jim would like to create a pencil holder with no top. He would like it to be 5 inches tall and 3 inches wide. He cannot decide if he would like to make it have a square base or a circular base. If the material costs $0.75 per square inch, hom much more would it cost to make a cylinder than a square prism?

Answer 1

Answer:

$\ 11.13$

Step-by-step explanation:

step 1

Find the surface area of the cylinder

The surface area of the cylinder is equal to

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

we have

$r=3/2=1.5\ in$ ----> the radius is half the diameter

$h=5\ in$

assume

$\pi =3.14$

substitute

$SA=(3.14)(1.5)^{2} +2(3.14)(1.5)(5)=54.165\ in^{2}$

Find the cost

$54.165*(0.75)=\ 40.62$

step 2

Find the surface area of the square prism

The surface area of the prism is equal to

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

we have

$b=3\ in\\ h=5\ in$

substitute

$SA=(3)^{2} +4(3)(5)=69\ in^{2}$

Find the cost

$69*(0.75)=\ 51.75$

step 3

Find the difference of costs

$\ 51.75-\ 40.62=\ 11.13$