(i) 30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find : the total surface area

(ii) 30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find volume of the cylinder so formed.

Answers (1)

(i) Answer  : 9152\; cm^{2}

It is given that 30 circular plates are placed one above the other to form a cylindrical solid.

So we can see that the height of this cylindrical solid = total thickness of 30 circular plates placed one over the other

Given, thickness of one circular plate =3\; cm

Thickness of 30 circular plates =30 \times 3 = 90\; cm

Now, radius of circular plate, r = 14 cm

We know that

Total surface area of the cylindrical solid of formed will be equal to 2\pi r\left ( h+r \right )

Where r is its radius and h is the height. So, putting the above calculated values:

Total surface area       =2 \times \frac{22}{7}\times 14\left ( 90+14 \right )

                                    =44 \times 2\times 104

                                   =9152\; cm^{2}

Hence, the total surface area of the cylindrical solid is 9152\; cm^{2}.

(ii)

Answer : 55440\; cm^{3}

It is given that 30 circular plates are placed one above the other to form a cylindrical solid.

So we can see that the height of this cylindrical solid = total thickness of 30 circular plates placed one over the other

Given, thickness of one circular plate = 3 cm

Thickness of 30 circular plates =30 \times 3=90\; cm

Now, radius of circular plate, r = 14 cm

We know that

Volume of the cylinder so formed will be equal to \pi r^{2}h

Where r is its radius and h is the height. So, putting the above calculated values:

Volume of the cylinder =\frac{22}{7}\times (14)^{2}\times 90

                                     =\frac{22}{7}\times 14\times 14 \times 90

                                     =55440\; cm^{3}

Hence, the volume of the cylindrical solid is 55440\; cm^{3}

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