Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 in.

Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 in.

  1. [tex]\bf\green{QuestioN:-}[/tex]

    Find the volume of a right circular cone that has a height of 18.9 inches and a base with a circumference of 15 inches.

    [tex]\bf\blue{AnsweR:-}[/tex]

    As we know,

    Volume of right circular cone = ⅓ (Base area × Height)

    Where as,

    Base Area = π r^2

    Hence, Volume = ⅓ π r^2 h

    Here,

    Height = 18.9 inches

    Circumference of the base = 15 inches

    We know,

    Circumference = 2πr or πd

    [tex]\implies\bf{15 = \dfrac{22}{7}\times{r}}[/tex]

    [tex]\implies\bf{r = \dfrac{15\times7}{22}}[/tex]

    [tex]\implies\bf{r= 4.7\:inches}[/tex]

    Now we can see the volume of this right circular cone,

    Formula applied here = ⅓ π r^2 h

    Radius = 4.7 inches

    Height = 18.9 inches

    Volume = ⅓ π r^2 h

    [tex]\implies\bf{\dfrac{1}{3}\times\dfrac{22}{7}\times4.7^{2} \times18.9}[/tex]

    [tex]\implies\bf{\dfrac{22}{21}\times22.09 \times18.9}[/tex]

    [tex]\implies\bf{437.382\:cubic\;units}[/tex]

    The required answer for your question is,

    [tex]\Large\pink\pmb{\bigstar437.382\:cubic\:units!!}[/tex]

    All Done!! ☺

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