Question

$50$ circular plates each of radius $7\mathrm{cm}$ and thickness $\frac{1}{2}\mathrm{cm}$ the are placed one above another to form a solid right circular cylinder. Find total surface area and volume of cylinder so formed.

Answer 1

Step 1: Interpret the data

Radius of the circular plate, $r=7\mathrm{cm}$ .

Thickness of the circular plate, $h=\frac{1}{2}\mathrm{cm}$.

Number of the circular plates, $n=50$.

The height of the cylinder will be the sum of the individual circular discs, i.e., $\frac{1}{2}+\frac{1}{2}+\dots 50\mathrm{times}=\frac{1}{2}\times 50=25\mathrm{cm}$.

Step 2: Calculate the Total surface area of cylinder

The formula for the surface area of a cylinder is given as,

$A=2\mathrm{\pi }r(h+r)$.

Where, $A$ is the surface area, $r$ is the radius of the cylinder and $h$ is the height of the cylinder.

Therefore, the surface area of the cylinder, $A=2\mathrm{\pi }\times 7\times (25+7)$

$=448\mathrm{\pi }{\mathrm{cm}}^2$

Step 3: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given as,

$V=\mathrm{\pi }{r}^{2}h$.

Where, $V$ is the surface area, $r$ is the radius of the cylinder and $h$ is the height of the cylinder.

Therefore, the volume of the cylinder, $V=\mathrm{\pi }\times 7^2\times 25$.

$=1225\mathrm{\pi }{\mathrm{cm}}^3$.

Therefore, the total surface area of the cylinder will be $448\mathrm{\pi }{\mathrm{cm}}^2$ and the volume will be $1225\mathrm{\pi }{\mathrm{cm}}^3$.