Question

The heights of two right circular cylinders are the same. Their volumes are respectively 16π m^3 and 81π m^3. The ratio of their base radii is
a) 16:81
b) 4:9
c) 2:3
d) 9:4



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Answer 1

Answer:

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Answer 2

Given:

The heights of two right circular cylinders are the same.

The volumes of two right circular cylinders are 16π m³ and 81π m³ respectively

To find:

The ratio of the base radii of two right circular cylinders.

Formula to be used:

Volume of cylinder = πr²h

Solution:

Step 1 of 2:

The heights of two right circular cylinders are the same.

$h_1 = h_2$

The volumes of two right circular cylinders are 16π m³ and 81π m³ respectively.

Volume of cylinder = πr²h

Volume of cylinder 1 = 16π m³

Volume of cylinder 2 =81π m³

Step 2 of 2:

Let,

$r_1$ and $r_2$ be the radius of cylinder 1 and cylinder 2,

Volume of cylinder 1 / Volume of cylinder 2 = $\frac{\pi r_{1} ^{2} h}{\pi r_{2} ^{2} h}$

$\frac{\pi r_{1} ^{2} h}{\pi r_{2} ^{2} h}$ = $\frac{16\pi }{81\pi }$

$(\frac{r_1}{r_2}) ^{2}$ =  $\frac{16}{81}$

$\frac{r_1}{r_2} = \sqrt{\frac{16}{81} }$

$\frac{r_1}{r_2} ={\frac{4}{9} }$

The ratio of their base radii is 4:9

Final answer:

The ratio of the base radii of two right circular cylinders is 4:9

Thus, the correct option is b) 4:9