Mathematics

Question

A can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company’s clients needs a cylindrical can that has the same volume but is 15 cm tall. What must the new radius be to meet the client’s need? Round to the nearest tenth of a centimeter. 2.7 cm 4.9 cm 7.3 cm 24.0 cm

2 Answer

  • Answer: Second option is correct.

    Explanation:

    Since we have given that

    Radius of cylinder (r)= 6 cm

    Height of cylinder (h) = 10 cm

    According to question, one of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall.

    So, Height of new cylinder (H)  = 15 cm

    Radius of new cylinder = R cm

    As we know the formula for " Volume of cylinder ":

    [tex]\pi r^2h=\pi R^2H\\\\6\times 6\times 10=R^2\times 15\\\\360=R^2\times 15\\\\\frac{360}{15}=R^2\\\\24=R^2\\\\\sqrt{24}=R\\\\4.9\ cm=R[/tex]

    Hence, Second option is correct.

  • The new radius needed to meet the client’s need is 4.9 cm.

    What is an equation?

    An equation is an expression that shows the relationship between two or more numbers and variables.

    The volume of the cylinder is:

    Volume = π * radius² * height

    For radius of 6 and height of 10 cm:

    Volume = π * (6)² * 10 = 360π cm³

    For a height of 15 cm:

    360π = π * (r)² * 15

    r = 4.9 cm

    The new radius needed to meet the client’s need is 4.9 cm.

    Find out more on equation at: https://brainly.com/question/2972832

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