Question

the radius and height of a cylinder are in the ratio 4:7 .find the radius and height of the cylinder if its volume is 1188 cu cm .also find it total surface area.

Answer 1

radius 1.5
height 6
TSA 622.3

Answer 2

Answer:

The radius of cylinder is 6 cm and height of the cylinder is 10.5 cm

The total surface area is 621.72 sq.cm.

Step-by-step explanation:

We are given that the radius and height of a cylinder are in the ratio 4:7

Let the ratio be x

So, radius = 4x

Height = 7x

Volume of cylinder =  $\pi r^{2} h$

                                =  $3.14 \times  (4x)^{2} (7x)$

                                =  $351.68x^3$

Since we are given that the volume of the cylinder is 1188 cu cm

So,  $1188=351.68x^3$

$\frac{1188}{351.68}=x^3$

$3.37807097361=x^3$

$1.5=x$

So, radius = $4x = 4 \times 1.5 = 6$

So, height = $7x = 7 \times 1.5 = 10.5$

Thus the radius of cylinder is 6 cm and height of the cylinder is 10.5 cm

Total surface area of cylinder = $2\pi r (h+r)$

                                                 = $2 \times 3.14 \times 6 (10.5+6)$

                                                 = $621.72 cm^2$

Hence the total surface area is 621.72 sq.cm.