Respuesta :

calculista

Answer:

The height of the can is [tex]h=9\ in[/tex]

Step-by-step explanation:

we know that

The surface area of the cylinder (can of peas) is equl to

[tex]SA=2\pi r^{2}+2\pi rh[/tex]

we have

[tex]SA=180.64\ in^{2}[/tex]

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.14[/tex]

substitute and solve for h

[tex]180.64=2(3.14)(2.5)^{2}+2(3.14)(2.5)h[/tex]

[tex]180.64=39.25+15.70h[/tex]

[tex]h=[180.64-39.25]/15.70[/tex]

[tex]h=9\ in[/tex]

Lanuel

The height of the can of peas is equal to 33.628 inches.

Given the following data:

  • Diameter of can = 5 inches.
  • Surface area of can = 180.64

[tex]Radius = \frac{5}{2} = 2.5\;centimeters.[/tex]

To calculate the height of the can of peas:

How to calculate surface area.

Note: A can of peas is cylindrical in nature.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex] SA = 2\pi rh + 2\pi r^2[/tex]

Where:

  • h is the height.
  • r is the radius.

Making h the subject of formula, we have:

[tex]h= \frac{SA-2\pi r^2 }{2\pi r} [/tex]

Substituting the given parameters into the formula, we have;

[tex]h= \frac{180.64-(2\times 2.5^2) }{2\times 2.5} \\ \\ h= \frac{180.64-(2\times 6.25) }{5} [/tex]

Height, h = 33.628 inches.

Read more on surface area here: https://brainly.com/question/21367171

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