Question

A cylindrical rod of height 10 m and radius 7m is melted into 7 identical cylindrical pistons of radius 14m and height $\frac{5}{14}$ m.

Decide whether or not the following assertions are correct:

(1) The volume of the cylindrical rod is equal to the sum of the volume of all 7 pistons.

(2) The total surface area of the cylindrical rod is equal to the sum of total surface area of the cylindrical piston.

Answer 1

Volume of the cylindrical rod = $\pi r^{2}h$

= $\frac{22}{7}\times 7\times 7\times 10$

= $1540m^3$

Volume of one cylindrical piston = $\pi r^{2}h$

=

$\frac{22}{\text{/}7}\times \text{/}{14}^2\times \frac{5}{\text{/}14}$

= 220 $m^3$

Volume of 7 cylindrical pistons = 7 $\times$220

=$1540m^3$

= Volume of cylindrical rod.

So, assertion 1 is correct.

Now,

Total surface area of cylindrical rod = $2\pi rh+2\pi r^2$

$2\times \frac{22}{\text{/}7}\times \text{/}7\times 10+2\times \frac{22}{7}\times 7\times 7$

= 440+308

=$748m^2$

Total Surface area of cylindrical piston = $2\pi rh+2\pi r^2$

$2\times \frac{22}{7}\times \text{/}14\times \frac{5}{\text{/}14}+2\times \frac{22}{7}\times 14\times 14$

=$\frac{220}{7}+\frac{8624}{7}$

= $\frac{8844}{7}{m}^2$

Total surface area of 7 cylindrical piston

= $7\times \frac{8844}{7}$

= $8844m^2$

So, assertions II is wrong.