A cone has a volume of 4000cm3 . Determine the height of the cone if the diameter of the cone is 30 cm. ​

Question

A cone has a volume of 4000cm3

. Determine the height of the cone if the diameter of the cone

is 30 cm. ​

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Cherry 2 weeks 2021-07-19T23:03:33+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-07-19T23:04:50+00:00

    Answer:

    17cm

    Step-by-step explanation:

    Given that the Volume of a cone is 4,000 cm³. And we need to determine the height of the cone , if the diameter is 30cm .

    Diagram :

    \setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17.5,1.6){\sf{15cm }}\put(9.5,10){\sf{17\ cm }}\end{picture}

    Step 1: Using the formula of cone :

    The volume of cone is ,

    \rm\implies Volume_{(cone)}=\dfrac{1}{3}\pi r^2h

    Step 2: Substitute the respective value :

    \rm\implies 4000cm^3 =\dfrac{1}{3}(3.14) ( h ) \bigg(\dfrac{30cm}{2}\bigg)^2

    As Radius is half of diameter , therefore here r = 30cm/2 = 15cm .

    Step 3: Simplify the RHS :

    \rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) (15cm)^2\\

    \rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) 225cm^2\\

    Step 4: Move all the constant nos. to one side

    \rm\implies h  =\dfrac{ 4000 \times 3}{ (3.14 )(225 )} cm \\

    \implies \boxed{\blue{\rm Height_{(cone)}= 16.98 \approx 17 cm }}

    Hence the height of the cone is 17cm .

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