Question

No. 8. The radius of the base and the height of a cylinder are 14 cm & 20 cm, respectively.
What is the volume of the cylinder?
No. 9. The ratio of the volumes of two cubes is 729:1331. What is the ratio of their total surface a​

Answer 1

Answer:

81:121 hope it helps you............

Answer 2

The  volume of the cylinder is $12,315.04\ cm^{3}$

The ratio of two cubes  total surface is $\frac{81}{121}$.

Step-by-step explanation:

Given:

The cylinder's the radius of the base and the height  are 14 cm & 20 cm, respectively.

The ratio of the volumes of two cubes is 729:1331.

To Find:

The  volume of the cylinder.

The ratio of two cubes  total surface.

Formula Used:

The volume of the cylinder V $=\pi p^{2} q$   -------------- formula no.01.

Where,

p=the cylinder's the radius of the base

q=the cylinder's the height

Volume of cube  $=side^{3}$

$\frac{V1}{V2} =\frac{m^{3} }{n^{3} }$    ------------------- formula no.02.

V1= volume of  the first cube.

V2=volume of  the second cube.

m= side of the first cube.

n=side of the second  cube

Total surface area of the  cube $=6\ side^{2}$

$\frac{S1}{S2} =\frac{6m^{2} }{6n^{2} }$   ----------------- formula no.03

S1= total surface area of  the first cube.

S2=Total surface area of the second cube.

Solution:

As given-The cylinder's the radius of the base and the height  are 14 cm & 20 cm, respectively.

p=14 cm   and q=20cm

Applying  formula no.01.

The volume of the cylinder V $=\pi p^{2} q$

                                                 $=\pi \times(14)^{2} \times20$

                                                 $=12,315.04\ cm^{3}$

Thus,the volume of the cylinder is $12,315.04\ cm^{3}$.

As given-the ratio of the volumes of two cubes is 729:1331.

$\frac{V1}{V2} =\frac{729}{1331}$

Applying formula no.02.

$\frac{V1}{V2} =\frac{m^{3} }{n^{3} }$

$\frac{729}{1331} =\frac{m^{3} }{n^{3} }$

$(\frac{9}{11} )^{3} = (\frac{m}{n} )^{3}$

$\frac{m}{n} =\frac{9}{11}$    ------------ equation no.01.

From formula no.03.

$\frac{S1}{S2} =\frac{6m^{2} }{6n^{2} }$

$\frac{S1}{S2} =(\frac{m}{n} )^{2}$

Putting the value of $\frac{m}{n}$ form equation no.01.

$\frac{S1}{S2} =(\frac{9}{11} )^{2}$

     $=\frac{81}{121}$  

Thus, the ratio of two cubes  total surface is $\frac{81}{121}$.    

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