Question

the radius of the base and the height of a cylinder are in the ratio 2 ratio 3 if its volume is 1617 cm cube find the total surface area of the cylinder

Answer 1

Given ratio = 2:3 and volume = 1617 cm^3.

Let the radius and height of the cylinder be 2x and 3x.   ---- (1)

Given volume of cylinder = 1617 cm^3

               pir^2h = 1617 cm^3

               (22/7) * (2x)^2 * 3x = 1617

                22/7 * 4x^2 * 3x = 1617

                x = 7/2.

Substitute x = 7/x in (1), we get

radius = 2 * 7/2 = 7

height = 3 * 7/2 = 21/2.

T.S.A of the cylinder = 2pir(h+r)

                                   = 2 * 22/7 * 7 * (21/2 + 7)

                                  = 22 * 35

                                  = 770 cm^2.

Answer 2

let radius be 2x and height be3x
volume =1617
$\pi {r}^{2} h = 1617 \\ \frac{22}{7} \times 2 {x}^{2} \times 3x = 1617 \\ \frac{22}{7} \times 4 {x}^{2} \times 3x = 1617 \\ \frac{22}{7} \times 12 {x}^{3} = 1617 \\ 12 {x}^{3} = \frac{1617 \times 7}{22 } \\ 12 {x}^{3} = 514.5 \\ {x}^{3} = \frac{514.5}{12} \\ {x}^{3} = 42.875 \\ x = 3.5$
r=3.5×2=7cm
h=3.5×3=10.5cm
Now,
TSA of cylinder = 2πr(r+h)
=
$2 \times \frac{22}{7} \times 7(7 + 10.5) \\ = 44 \times 17.5 \\ = 770 {m}^{2}$