Question

The ratio between the radius of the base and the height of a cylinder is 2:3. Find the total surface area of the cylinder if it's volume is 1617 cm^3

Answer 1

I hope it will help you

Answer 2

Answer:

538.836 sq.cm.

Step-by-step explanation:

The ratio between the radius of the base and the height of a cylinder is 2:3.

Let the ratio be x

So, radius = 2x

Height = 3x

Volume of cylinder = $\pi r^{2} h$

So, Volume of given cylinder = $\pi (2x)^{2} (3x)$

Now we are given that volume is 1617 cubic cm.

So,  $1617=3.14 \times 12x^3$

$1617=37.68x^3$

$\frac{1617}{37.68}=x^3$

$42.91401=x^3$

$\sqrt{3}{42.91401}=x$

$3.50106=x$

So, Radius = $2x = 2\times 3.50106 =7.00212 cm$

Height =  $3x = 3 \times 3.50106 =10.50318 cm$

Total Surface area of cylinder = $2\pi rh+2\pi r^{2}$

                                                   = $2(3.14)(7.00212)(10.50318)+2(3.14)(7.00212)^{2}$

                                                   = $2538.836 cm^2$

Hence the total surface area of cylinder is 538.836 sq.cm.