Question

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is 8316 cm³, find the total surface area of the cylinder.

Answer 1

It is given in the question that, 

The ratio of radius and height is 7 : 2 

This means that,

\(\frac{radius}{height}=\frac{7}{2}\)

\(\frac{r}{h}=\frac{7}{2}\)

\(r=\frac{7}{2}h\)

Now, 

We can find the volume of the cylinder as: 

Volume of the cylinder = \(\pi r^2h\)

8316 = \(\pi (\frac{7}{2}h)^2h\)

8316 = \(\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\times h^3\)

h³ = \(\frac{8316\times2}{11\times7}\)

h³ = 216

h = 6 

Hence, 

Radius, r = \(\frac{7}{2}h\)

= \(\frac{7}{2}\times6\)

= 21 cm

Therefore, 

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

= \(2\times\frac{22}{7}\times21\times27\)

= 2 × 22 × 3 × 27

= 3564 cm²