Question

a metal cylindrical disc of base radius 28cm and height 7 cm is melted and recast into a cylindrical block of base radius 14 cm. find the length of a cylindrical block of a find the ratio and find the total surface area of the cylindrical disc to that of the block.

Answer 1

Therefore the length of the cylindrical block is=28 cm

Therefore the ratio of total surface area of the cylindrical disc to cylindrical block=5:3

Step-by-step explanation:

Given , A metal cylindrical disc of base radius 28 cm and height 7 cm .

Therefore the volume of the cylindrical disc

$=\pi r^2 h$

$=\pi \times 28^2\times 7$ cm³

Therefore total surface area of the cylindrical disc

$=2\pi r(r+h)$

$=2\pi \times 28(28+7)$

$=2\pi \times 28 \times 35$ cm²

Let the height of the new cylindrical block be h

Then the volume of the cylindrical block is

$=\pi r^2 h$

$= \pi \times 14^2 \times h$ cm³

According to the problem

$\pi \times 28^2\times 7 = \pi \times 14^2 \times h$

$\Leftrightarrow h=\frac{\pi \times 28^2\times 7}{\pi\times 14^2}$

$\Leftrightarrow h=28$

Therefore the length of the cylindrical block is=28 cm

The total surface area of cylindrical block

$=2\pi r(r+h)$

$=2\pi \times 14(14+28)$

$=2\pi \times 14 \times 42$ cm²

Therefore the ratio of total surface area of the cylindrical disc to cylindrical block$=(2\pi \times 28 \times 35):(2\pi \times 14 \times 42)$

                                 =5:3

Answer 2

Answer:

hay mate it is a very simple question it's all dependent upon formula and according to your question I think you are in class 8 so you should know this that how to solve this question anyways I am just solving this and giving you the explanation on a page and even I will just tell you something more......

Step-by-step explanation:

so according to the solution provided by me you have to first of all find the height of the cylindrical block which is 28 CM

then the second thing which you have to do is to find the total surface area of cylinderycal block

and the next step will be to find the total surface area of cylinderycal disc

and as you got the answers of of the total surface area of cylinderycal block as well as cylindrical disc

so with the question which you asked was to find the ratio of the total surface area of the block to the disc

so the next step which you will do is do divide 6160 upon 3696

don't do the mistake of using the calculator because it will give the answer of the division of the numbers

you have to do it with your own

here you find the ratio which will be 5 ratio 3 which is the answer of your question

so as the answer which I provided this was so easy for me to find the answer because it was too easy question and even I am also in class 8 and I am just doing the chapter one right now playing with numbers but it's too easy to solve this question for me

but it's ok everyone has different capability

please do it well ..

keep studying ...

be intelligent and excellent , amazing and wonderful

and also for your question I did a hard task so please mark me as brainlist and I will be satisfied by that only....