Question

3) Mr. Brust is addicted to Red Bull and has decided that he wants to plaster his room at school with Red Bull cans.
He measures a can and finds it is 6.5 inches tall and has a diameter of about 2.5 inches. He decided that he will
just recycle the top and bottom since there is no Red Bull logo on them and just use the sides. How many cans will
Mr. Brust need to cover his wall that is 20 feet long and 9 feet tall?

Answer 1

Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.

What is area of rectangle?

Area of rectangle is the product of its sides

i.e., Area of rectangle = length  x breadth

What is area of circle?

The area of a circle is pi times the radius squared (A = π r²).

What is circumference of circle?

The circumference of a circle is defined as the linear distance around it.

( C= 2πr)

The can of red bull is in shape of cylinder.

If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.

Like the given figure given.

• The can is 6.5 inches tall and has a diameter of about 2.5 inches.

 

It shows that the two circle will have the diameter 2.5 inches.

d= 2.5 inch

 = 0.208 ft

radius, r= $\frac{d}{2}$

r= $\frac{0.208}{2}$

r= 0.104 ft

• To get the length of the rectangle , we have to calculate the circumference of the circle.

Circumference of the circle be,

= 2πr

= 2 x 3.14 x 0.104

= 0.653 ft

The rectangular sheet will have,

length=  0.653 ft, breadth= 6.5 inches = 0.541 ft

• Now, area of rectangular sheet be,

      = length x breadth

      = 0.653 x 0.541

      =$0.3532 ft^{2}$

• Area of 2 circle( top and bottom of can) be,

       = 2 x π$r^{2}$

       = 2 x 3.14 x 0.104 x 0.104

       = 6.28 x 0.010816

       = 0.0679 $ft^{2}$

• Total area of can be,

        = Area of rectangular sheet + Area of 2 circle( top and bottom of can)

        = 0.3532 + 0.0679

        = 0.4211 $ft^{2}$

Now, we have the wall of dimensions

length= 9 ft, breadth= 20 ft

• Area of wall be,

= length x breadth

=9 x 20

= 180 $ft^{2}$

• Number of cans required to cover the whole wall be,

         =$\frac{area \;of\; wall}{area \;of\; can}$

         =$\frac{180}{0.4211}$

         = 427.45 cans

         ≈ 428 cans

Learn more about the concept of area here:

https://brainly.com/question/16193772

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