Question

A cone has a volume of 4000cm3

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

is 30 cm. ​

Answer 1

17cm

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))=(1)/(3)\pi r^2h`

Step 2: Substitute the respective value :-

`\rm\implies 4000cm^3 =(1)/(3)(3.14) ( h ) \bigg((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 = (1)/(3)(3.14) ( h ) (15cm)^2\\`

`\rm\implies 4000 cm^3 = (1)/(3)(3.14) ( h ) 225cm^2\\`

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

`\rm\implies h =( 4000 * 3)/( (3.14 )(225 )) cm \\`

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

Hence the height of the cone is 17cm .