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RD Sharma Solutions Class 8 Mathematics Solutions for Volume Surface Area Cuboid Cube Exercise 21.4 in Chapter 21 - Volume Surface Area Cuboid Cube
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A closediron tank 12 m long, 9 m wide and 4 m deep is to be made. Determinethe cost of iron sheet used at the rate of Rs. 5 per metre sheet, sheet being 2 m wide.
Answer:
Given,
Length of tank, l = 12 m Width of tank, b = 9m
Depth of tank, h = 4m
Area of sheet required = total surface area of tank
= 2 (lb×bh×hl)
= 2 (12×9 + 9×4 + 4×12)
= 2 (108 + 36 + 48)
= 2 (192)
= 384 m2
Let length be l1
Breadth be b1 Given, b1 = 2m l1 × b1 = 384
l1 = 384/b1
= 384/2
= 192m
∴ Cost of iron sheet at the rate of Rs 5 per metre = 5 × 192 = Rs 960
Video transcript
[Music] hello dear student i am sunita nair from dido learning and i am here to help you with this sum which goes like this a closed iron tank 12 meters long 9 meters wide and 4 meters deep is to be made determine the cost of iron sheet used at the rate of 5 per meter the sheet being 2 meters wide all right so these are the details which are given to us so let's start working on the sum now the dimensions of the ion tank are given to us so let's note them down the length of the ion tank right the length is given as 12 meters the width is given as 9 the width is given as 9 so let's mark that up that's nine and the height is given as four meters deep deep is another word for height so let's mark that the height is given as 4 meters all right so this is 4 meters okay so here we are concerned with uh we are concerned with the surface area because we have to know the area because we need to we need to use the area measurements to make the iron tank right we need to know the surface area measurements so let us calculate that now we know that the surface area right the total surface area of of a cuboid would be 2 into l into b plus b into h plus l into h right this is the formula for the total surface area so let's note down these dimensions the length is given as 12 the breadth of width is given as 9 and the height or the depth is given as 4 right so total surface area is equal to tsc's total surface area is equal to 2 multiplied by l into b that is 12 into 9 plus b into h that is 9 into 4 plus l into h that is 12 into 4 which is equal to 2 multiplied by 12 into 9 is one zero eight nine into four is thirty six and twelve into four is forty eight so we get a total of two into 8 and 8 16 16 and 6 is 22 we carry the 2 here 4 into 6 and 3 9 one hundred and ninety two two into one hundred and ninety two is two twos are four two nines are eighteen two ones are two and one three this is the total surface area of the rectangular closed ion tank all right now we have to buy the iron sheet for this area from a shop that sells it in this form in the form of a sheet right in the form of a sheet whose width is 2 meters wide so this is 2 meters wide right so this is 2 meters wide and we need to find this length we need to find the length of the iron sheet right so we need to find the length because the the rectangular sheet is sold is sold by length right so many meters are sold so the width is not taken into consideration while quoting the price they quote the price according to the length of the sheet all right so now for this area for this area of iron sheet we need to find what will be the length that is required because we know the width is going to be 2 meters we need to find the length so let's work that out so this 384 right would be equal to 2 multiplied by the length right whatever length of sheet we have to buy the width is given as 2 we need to find the length so what will the length be so length will be 384 divided by 2 which is 192 meters so basically we have to buy 192 meters length of iron sheet now let's find out the cost the cost would be the cost is at the rate of 5 meters i am sorry 5 rupees per meter so cost at 5 rupees per meter would be equal to 5 into 192 which is equal to five twos are ten five nines are forty five and one forty six five ones are five and four nine right so this is the cost i'll put rupees 960 here so our answer is 960 rupees for the cost of iron sheet to make the tank of the given dimensions i hope you understood the explanation do drop a comment in the comment section if you have any doubts visit our channel regularly for more homework solutions like this and subscribe to it for updates thank you
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