Question

radius of the base and the height of a cylinder are in the ratio 2:3 if the volume of the cylinder is 1617 cm square .calculate its total surface area

Answer 1

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Given;

Radius : Height = 2 : 3.

=> 3r = 2h

=> h = 3r / 2.

Now,

Volume Of Cylinder = 1617 cm^3.

$= > \pi \times {r}^{2} \times h$

=> 22 / 7 × r × r × 3r/2 = 1617

=> r^2 × 3r/2 =( 1617 × 7)/22

=> r^3 = (1617 × 7 × 2)/ 22 × 3

=> r^3 = 343

$= > r = \sqrt[3]{343}$

=> r = 7 cm.

Now,

Height = 3r / 2

=> h = 21/2

=> h= 10.5 cm.

Now,

Surface Area of Cylinder

$= > 2\pi \times r(r + h)$

=> 2 × 22/7 × 7 ( 7 + 10.5)

=> 44 × 17.5

=> 770 cm^2.
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