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Thread: surface areas and volumes

  1. #1
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    surface areas and volumes

    how much will the volume of sphere be reduced if radius of sphere is halfed?
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  2. #2
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    Quote Originally Posted by anjana View Post
    how much will the volume of sphere be reduced if radius of sphere is halfed?
    Hello, Anjana,

    let $\displaystyle r_1=r$ and $\displaystyle r_2=\frac{1}{2}r$

    Then you have $\displaystyle V_1=\frac{4}{3} \pi r^3$ and
    $\displaystyle V_2=\frac{4}{3} \pi (\frac{1}{2}r)^3$ . Expand:
    $\displaystyle V_2=\frac{4}{3} \pi \frac{1}{8}r^3=\frac{1}{8} \cdot \frac{4}{3} \pi r^3$

    Now compare $\displaystyle V_1\ \text{and} \ V_2$

    EB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by anjana View Post
    how much will the volume of sphere be reduced if radius of sphere is halfed?
    As a rule the volume of similar solids scales as the cube of corresponding
    linear dimensions, so halving the radius scales the volume by (0.5)^3.

    RonL
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