Question

The radius and height of a cylinder are in the ratio 7 is to 9 if the volume of cylinder is 1386 find the total surface area of the cylinder

Answer 1

Answer:

704 cm²

Step-by-step explanation:

Given---> Ratio between radius and height of a cylinder is 7:9 and volume of cylinder is 1386 cm³

To find---> Total surface area of cylinder

Solution---> Let radius and height of cylinder be r and h respectively.

ATQ,

Ratio between radius and height of cylinder is 7:9.

So , r : h = 7 : 9

Let , r = 7x and h = 9x

ATQ, Volume of cylinder = 1386

=> π r² h = 1386

=> 22/7 × ( 7x )² × 9x = 1386

=> 22/7 × 49 x² × 9x = 1386

=> 22 × 7 × 9 x³ = 1386

=> x³ = 1386 / 22×7×9

=> x³ = 1386 / 1386

=> x³ = 1

=> x³ = 1³

=> x = 1

Now, radius of cylinder = 7x = 7 ( 1 ) = 7 cm

Height of cylinder = 9x = 9 ( 1 ) = 9 cm

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

= 2 × ( 22/7 ) × 7 × ( 7 + 9 )

= 2 × 22 × 16

= 704 cm²

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