Get the answer to "The diameter of two cylinder are in the..."

Yandel Hunter

Answered question

2022-02-10

The diameter of two cylinder are in the ratio of

2 : 3

. What will be the ratio of their heights if their volumes are equal?

kuwebux78

Beginner2022-02-11Added 13 answers

Step 1
Let the ratio of height of two cylinders be

k : 1

, say heights are kh and h
As diameters are in the ratio of

2 : 3

, let diameters be 2d and 3d
Hence their volumes are

π {(\frac{2 d}{2})}^{2} \times k h = π k h d^{2}

and

π {(\frac{3 d}{2})}^{2} \times h = \frac{9 π}{4} h d^{2}

As two volumes are equal, we have

π k h d^{2} = \frac{9 π}{4} h d^{2}

k = \frac{\frac{9 π}{4} h d^{2}}{π h d^{2}} = 9 : 4

Hence ratio of their heights is

9 : 4

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