Question

Find ratio of radii of two cylinders if ratio of heights are in 4:7 and ratio of their volumes are in 36:175

4:5


3:5


3:7


6:7​

Answer 1

Step-by-step explanation:

Ratio in radii = 2:3

and in heights = 5:3

Let

r

1

,

h

1

and

r

2

,

h

2

are the radii and heights of two cylinders respectively.

∴

r

1

r

2

=

2

3

and

h

1

h

2

=

5

3

Now

Volume~of~first~culinder

Volume~ of~second~cylinder

=

π

(

r

1

)

2

h

1

π

(

r

2

)

2

h

2

(

r

1

r

2

)

2

×

(

h

1

h

2

)

=

(

2

3

)

2

×

5

3

=

4

9

×

5

3

=

20

27

Answer 2

Given-

Radii of two cylinders if the ratio of heights are in 4:7 and the ratio of their volumes are in 36:175

To Find-

The ratio of radii of two cylinders

Solution-

The volume of the cylinder is пr²h

Let the height of the two cylinders be 4x and 7x.

So, their volume be пr₁²4x and пr₂²7x

The volume ratio is 36:175

So,$\frac{4r1r1}{7r2r2}$=$\frac{36}{175}$

Now the ratio of two-cylinder is r₁/r₂=$3/5$

Hence, the ratio of the two cylinders is 3:5.