Question

A photo of size $14cm{\text{ by }}10cm$ is to be framed by taking the margin of $1cm$ along each side of the photo. Find the area of the margin and also find the cost of framing the photo at the rate of ${\text{Rs 8}}{\text{.80 per }}c{m^2}$

Answer 1

Hint:
As we know that the dimensions of the photo that is length$ = 14cm$ and breadth$ = 10cm$ and hence we can say that it is a 2D photo and hence its area is given as ${\text{length }} \times {\text{ breadth}}$ and we need to frame by taking the margin of $1cm$so its dimensions become $16cm{\text{ by }}12cm$

Complete step by step solution:
Here in this question we are given that a photo of size $14cm{\text{ by }}10cm$ is to be framed by taking the margin of $1cm$ along each side of the photo.
So we are given the dimensions of the photo that is
Length$ = 14cm$ and breadth$ = 10cm$
Now we need to frame the photo by taking the margin of $1cm$ along each side of the photo. So now let us draw the diagram:

Let here $ABCD$ is the photo of the dimensions $14cm{\text{ by }}10cm$ and $PQRS$ is the frame of the photo such that $1cm$ is left along each of the four sides and we need to find the area of framing the photo and the rate is given as ${\text{Rs 8}}{\text{.80 per }}c{m^2}$
As we know that the length of the photo which is $AB = 14cm$ and the breadth of the photo which is $BC = 10cm$
Now we put the margin along all the four sides of the photo of the length $1cm$ so the new dimensions of the figure becomes
$
\Rightarrow PQ = AB + {\text{twice the thickness}} \\
\Rightarrow {\text{ = 14 + 2}} \\
\Rightarrow {\text{ = 16}}cm \\
 $
And $
\Rightarrow QR = BC + {\text{twice the thickness}} \\
\Rightarrow {\text{ = 10 + 2}} \\
\Rightarrow {\text{ = 12}}cm \\
 $
Now we know that area is given by ${\text{length }} \times {\text{ breadth}}$
So area of the photo
Now area of the plate along with the frame = area of PQRS = $16 \times 12 = 192 cm^2$$ = 14 \times 10 = 140c{m^2}$
So the area required$ = {\text{ area of the photo with the frame - area of the photo}}$
So area$ = 192 - 140 = 52c{m^2}$
And as we know the cost of framing the $1c{m^2}{\text{ is Rs 8}}{\text{.80}}$
So for $52c{m^2} = {\text{Rs}}(52)(8.80)$

So the cost of framing is ${\text{Rs 457}}{\text{.6}}$

Note:
If we are given to find the capacity of any item then we need to find its volume and we know the volume of the cuboid$ = ({\text{length}})({\text{breadth)}}({\text{height}})$ and the volume of the cube$ = {({\text{length)}}^3}$