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azamat
3 years ago
12

Jim would like to create a pencil holder with no top. He would like it to be 5 inches taller and 3 inches wide. He can't decide

if he would like to make it a square base or a circular base. If the material costs $0.75 per square inch, how much more would it cost him to make a square prism than a cylinder?
Mathematics
1 answer:
irakobra [83]3 years ago
4 0

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}

<em>Find the cost</em>

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}

<em>Find the cost</em>

69*(0.75)=\$51.75

step 3

Find the difference of costs

\$51.75-\$40.62=\$11.13

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Long N. answered • 10/06/16

TUTOR  4.5 (4)

Years of Tutoring Calculus, Algebra, Statistics, Finance and SAT Prep

SEE TUTORS LIKE THIS

For the fixed given perimeter, the maximum area which can be obtained is a square.

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