Answer
Verified
480k+ views
Hint: First of all, get the area of the plastic sheet required by filling the total surface area of the open box that is \[S=2\left( hb+hl \right)+lb\] and then multiply this area with the cost of sheet per \[{{\text{m}}^{2}}\] to get the total cost of sheet.
Complete step-by-step answer:
We are given a plastic box of length, breadth and height equal to 1.5 m, 1.25 m and 65 cm respectively. It is opened at the top. We have to find the area of the sheet. Also, we have to find the cost of the sheet if the sheet costs Rs. 20/\[{{\text{m}}^{2}}\].
(i) First of all, we have to find the area of the sheet required to make this box. To get the total area of the sheet required, we have to find the total surface area of the given box. Let us consider the surface area of the box to be S.
We know that this box is in the shape of a cuboid. So, the total surface area of cuboid = 2 (lb + bh + hl) where l, b and h are the length, breadth and height of the cuboid.
But as we are given that this box is an open box that is it is open at the top. So, we must subtract the area of the upper face from the total surface area of the cuboid to get the required surface area of the given box. So, we get
Surface area of box (S) = 2 (lb + bh + hl) – (Area of the upper face)
We know that area of the upper face of box = l x b
So, we get, S = 2(lb + bh + hl) – lb
Therefore, we get surface area of the box (S) = 2 (bh + hl) + lb …..(1)
Now, we know that the area of the plastic sheet required = Surface area of box (1)
So, now we substitute the length of box = 1.5 m, breadth of the box = 1.25 m and height of the box = 65 cm = 0.65 m in equation (1) to get the plastic sheet required. So, we get,
S = Area of plastic sheet required \[=2\left[ \left( 1.25\times 0.65 \right)+\left( 0.65 \right)\left( 1.5 \right) \right]+\left( 1.5\times 1.25 \right)\text{ }{{\text{m}}^{2}}\]
\[S=\left[ 2\left( 0.8125+0.975 \right)+1.875 \right]\text{ }{{\text{m}}^{2}}\]
\[S=5.45\text{ }{{\text{m}}^{2}}\]
So, we get the area of the plastic sheet required to make the given box equal to \[5.45\text{ }{{\text{m}}^{2}}\].
(ii) Now, we are given that, cost of sheet = Rs.20/\[{{\text{m}}^{2}}\]
So, to get the total cost of the sheet required, we have to multiply the area of the total sheet required with cost of the sheet per \[{{\text{m}}^{2}}\]. So, we get,
Total cost of the sheet required to make this box = Rs (20 x 5.45) = Rs.109.
So, we get the total cost of the sheet to make this as equal to Rs.109.
Note: Here, many students forget to subtract the area of the upper face of the cuboid box. So, this must be kept in mind whenever the box is open. Also, students must note that whenever we calculate the surface area, volume etc. of any object, we must substitute length, breadth and height in the same unit. In this question, we can see that the given height is in centimeters. So, we must first convert it into meters and then only substitute it to get the surface area.
Complete step-by-step answer:
We are given a plastic box of length, breadth and height equal to 1.5 m, 1.25 m and 65 cm respectively. It is opened at the top. We have to find the area of the sheet. Also, we have to find the cost of the sheet if the sheet costs Rs. 20/\[{{\text{m}}^{2}}\].
(i) First of all, we have to find the area of the sheet required to make this box. To get the total area of the sheet required, we have to find the total surface area of the given box. Let us consider the surface area of the box to be S.
We know that this box is in the shape of a cuboid. So, the total surface area of cuboid = 2 (lb + bh + hl) where l, b and h are the length, breadth and height of the cuboid.
But as we are given that this box is an open box that is it is open at the top. So, we must subtract the area of the upper face from the total surface area of the cuboid to get the required surface area of the given box. So, we get
Surface area of box (S) = 2 (lb + bh + hl) – (Area of the upper face)
We know that area of the upper face of box = l x b
So, we get, S = 2(lb + bh + hl) – lb
Therefore, we get surface area of the box (S) = 2 (bh + hl) + lb …..(1)
Now, we know that the area of the plastic sheet required = Surface area of box (1)
So, now we substitute the length of box = 1.5 m, breadth of the box = 1.25 m and height of the box = 65 cm = 0.65 m in equation (1) to get the plastic sheet required. So, we get,
S = Area of plastic sheet required \[=2\left[ \left( 1.25\times 0.65 \right)+\left( 0.65 \right)\left( 1.5 \right) \right]+\left( 1.5\times 1.25 \right)\text{ }{{\text{m}}^{2}}\]
\[S=\left[ 2\left( 0.8125+0.975 \right)+1.875 \right]\text{ }{{\text{m}}^{2}}\]
\[S=5.45\text{ }{{\text{m}}^{2}}\]
So, we get the area of the plastic sheet required to make the given box equal to \[5.45\text{ }{{\text{m}}^{2}}\].
(ii) Now, we are given that, cost of sheet = Rs.20/\[{{\text{m}}^{2}}\]
So, to get the total cost of the sheet required, we have to multiply the area of the total sheet required with cost of the sheet per \[{{\text{m}}^{2}}\]. So, we get,
Total cost of the sheet required to make this box = Rs (20 x 5.45) = Rs.109.
So, we get the total cost of the sheet to make this as equal to Rs.109.
Note: Here, many students forget to subtract the area of the upper face of the cuboid box. So, this must be kept in mind whenever the box is open. Also, students must note that whenever we calculate the surface area, volume etc. of any object, we must substitute length, breadth and height in the same unit. In this question, we can see that the given height is in centimeters. So, we must first convert it into meters and then only substitute it to get the surface area.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE