Algebra

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A cone has a radius of 15 cm and a volume of 540 cm3. Find the volume of a similar cone with a radius of 10 cm.

A. 54 cm^3
B. 240 cm^3
C. 16 cm^3
D. 360 cm^3

I think its D but by the process of elimination...don't know how to figure it out really...?

  • Algebra -

    Could Answer c be 160 cm^3 and not 16 cm^3?

  • Algebra -

    yes it is sorry.

  • Algebra -

    The answer would then be C. 160 cm^3
    The Volume of a cone is given by
    V=(1/3)*pi*r^2*h

    We know V= 540 cm^3 and that r=15 cm and can plug into the equation to find h.
    I am going to leave the units off, but you should include it in your work.
    540=(1/3)*pi*(15)^2*h
    Solving for h gives
    h=2.292 cm

    Now a similar cone will have the same ratio

    h1/r1 = h2/r2
    (2.292 / 15) = (h2 / 10) and solve for h2.
    h2 = 1.528 cm
    Throw this into the Volume of a cone
    V=(1/3)*pi*r^2*h
    V=(1/3)*pi*(10)^2*(1.528) = 160 cm^3

  • Algebra -

    simpler way:
    the volume of 2 similar solids is proportional to the cube of their sides

    V/540 = 10^3/15^3
    V = 540(1000)/(3375) = 160

  • Algebra -

    Thank you both...

  • Algebra -

    c i got 100%

  • Algebra -

    if you go to connexus academy the anwsers for the test are
    D
    B
    C
    A
    A
    C

  • Algebra -

    can someone give me the awnsers of the whole test i am in conections academy to.

  • Algebra -

    Yeah does anyone have the answers to the whole test

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