Name: Volume of a Cylinder: Examples
Uploaded: 2019-07-19
Duration: 3 min 51 s
Description: Need to know how to find the volume of a cylinder? Well, you're in the right place! In this video, we look at how to find the volume of a cylinder through some examples.

Question

A metal cylindrical disc of base radius $4 cm$ and height $1.5 cm$ is melted and recast into a cylindrical bar of base radius $2 cm$ . Find the ratio of the total surface area of the disc to that of the bar.

Question Image

Accepted Answer

We know that the volume and the total surface area of a cylinder are given by ${πr}^{2} h$ and $2 πr (r + h)$ , where $r$ is the radius and $h$ is the height of the cylinder.

The volume of the cylinders will remain the same when the disc is recast into the bar. Here, both the disc and the bar are cylinders.

Let the radius and height of the disc be $r$ and $h$ , respectively. So, $r = 4 cm, h = 1.5 cm$ .

Let the radius and height of the bar be $R$ and $H$ , respectively. Here, $R = 2 cm$ .

So, we get, $π \times {(2)}^{2} \times H = π \times {(4)}^{2} \times 1.5$

$\Rightarrow H = \frac{π \times (4)^{2} \times 1.5}{π \times (2)^{2}}$

$\Rightarrow H = \frac{4 \times 4 \times 1.5}{2 \times 2} = 6 cm$

So, the height of the cylinder that is recast is $6 cm$ .

Now, the ratio of the total surface area of the disc to that of the bar is $\frac{2 πr (r + h)}{2 π R (R + H)}$

$= \frac{r (r + h)}{R (R + H)} = \frac{4 (4 + 1.5)}{2 (2 + 6)} = \frac{4 \times 5.5}{2 \times 8} = \frac{5.5}{4} = \frac{55}{40} = \frac{11}{8} = 11 : 8$ .

Therefore, the required ratio of the total surface area of the disc to that of the bar is $11 : 8$ .

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