Question

R K Agrawal is designing a propylene tank in the shape of a cylinder with hemispherical ends. If the length of the cylinder is to be 20 unit larger than its radius and the volume is to be 3321π cubic unit, then find the radius.And please give me the step by step explaination,not only the answer

Answer 1

Step-by-step explanation:

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Answer 2

Given:

Length of the cylinder=20 units larger than the radius

Volume=3321π cubic units

To find:

The radius of the tank

Solution:

We can find the radius by following the steps given below-

We know that the tank is a cylinder with two hemispheres at each end.

The total volume of the tank= Volume of cylinder+ 2×Volume of the hemisphere

Let the radius of the cylinder be R.

The height of the cylinder, H= R+20 units

So, the total volume=

$π {R}^{2} H +2×2/3π {R}^{3}$

$3321\pi = \pi {R}^{2} (R + 20) + 4 /3\pi( {R}^{3} )$

$3321 = {R}^{2} (R + 20) + 4 \div 3 {R}^{3}$

$3321 \times 3 = 3 {R}^{2} (R + 20) + 4 {R}^{3}$

$3321 \times 3 = 3 {R}^{3} +60 {R}^{2} + 4 {R}^{3}$

$3321 \times 3 = 7 {R}^{3} + 60 {R}^{2}$

$3321 \times 3 = {R}^{2} (7R + 60)$

Now, we will factorize the LHS till we get the values that fit the equation.

$81 \times 123 = {R}^{2} (7R + 60)$

Here,

${R}^{2} = 81 \: and \: 7R + 60 = 123$

So, R=9 units

Therefore, the radius of the tank is 9 units.