Question

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Answer 1

Question;


Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

$\mathsf{solution}$


Revision of Formula;

Total surface area of solid cylinder= 2πr(h+r)

Lateral surface area of the curved surface area of cylinder= 2πrh

Note:-

The volume of cylinder B is Greater then Volume of Cylinder A.

According to the Question;

Diameter of cylinder A = 7 cm

Radius of cylinder A = 7/2 cm

And Height of cylinder A = 14 cm

According to the Formula of Volume of cylinder = π²rh


Volume of cylinder A = πr²h


$\implies \: \tt \frac{22}{7} \times { ( \frac{7}{2} )}^{2} \times 14 \\ \\ \\ \tt \implies \: \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 14 \\ \\ \\ \sf \implies \: \implies \: \frac{22}{ \cancel7} \times \frac{ \cancel7}{ \cancel2} \times \frac{7}{2} \times \cancel{14} \\ \\ \\ \sf\implies22 \times \frac{49}{2} \\ \\ \red{ \implies \: 539} {cm}^{3}$
Hence, Volume of cylinder A= 539cm³




Diameter of cylinder B = 14 cm

Radius of cylinder B = 14/2 cm
= 7cm


And Height of cylinder B = 7 cm



According to the Formula of Volume of cylinder = π²rh


Volume of cylinder B = πr²h


= 22/7 ×(7)² × 7

= 22/7 ×7× ×7

= 1078 cm³

Here, Volume of Cylinder B is greater than Volume of Cylinder A.


Again According to the Question!


Total surface area of solid cylinder= 2πr(h+r)

$\implies \: \sf \large{(}2 \times \frac{22}{7} \times \frac{7}{2} \ \large( \frac{7}{2} + 14 \large)$

$\implies \: (22 \times ( \frac{7 + 28}{2} ) {cm}^{2} \\ \\ \implies \: (22 \times \frac{35}{2} ) \\ \\ \\ \implies \: ( \cancel{22} \times \frac{35}{ \cancel{2}} ) \\ \\ \\ \\ \implies \: 35 \times 11 = 385 \: {cm}^{2}$


Here, Surface Area of Cylinder A= 385 cm²


Again, Surface Area of Cylinder B = 2πr(r+h)



$\implies \sf\: 2 \times \frac{22}{7} \times 7 \times (7 + 7) \\ \\ \\ \\ \sf \implies \: 44 \times 14 {cm}^{2} \\ \\ \sf \implies \: 616 {cm}^{2}$


[From Above Explaination ,The surface area of cylinder B is also greater than the surface area of cylinder A.]