Question

The heights of two right circular cylinders are the same. Their volumes are respectively 25π m³ and 81π m³. The ratio of their base radii is​

Answer 1

Solution

Given :-

• The heights of two right circular cylinders are the same
• Their volumes are respectively 25π m³ and 81π m³.

Find :-

• Ratio of their Base Radii

Explanation

Let,

• Base radii of first right circular cylinder = r
• Base radii of second right circular cylinder= r'
• Height of first right circular cylinder = h
• Height of second right circular cylinder = h'

Using Formula

$\dag\boxed{\underline{\tt{\orange{\: Volume_{right\: circular\: cylinder}\:=\:\pi\:r^2\:h}}}}$

Then,

• Volume of first right circular cylinder = πr²h
• Volume of second right circular cylinder = πr'²h'

So, Now

==> (πr²h/πr'²h') = 25/81

==> r²h/r'²h' = 25/81

But, Here

• h = h'

Then,

==> πr²h/πr'²h = 25/81

==> r²/r'² = 25/81

==> (r/r')² = 25/81

==> r/r' = √(25/81)

==> r/r' = √(5×5)/(9×9)

==>r/r' = 5/9

Hence

• Ratio of their radii will be = 5:9

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