Ex.13.1 Q4 Surface Areas and Volumes - NCERT Maths Class 9

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Question

The paint in a certain container is sufficient to paint an area equal to \(\begin{align} 9.375\,\rm{m^2} \end{align}\). How many

bricks of dimensions

\(\begin{align} 22.5 \rm{cm} \times 10 \rm{cm} \times 7.5 \rm{cm} \end{align}\) can be painted out of this container?

 Video Solution
Surface Areas And Volumes
Ex 13.1 | Question 4

Text Solution

Reasoning:

Brick is nothing but a cuboid having six faces. Surface area of the brick is the sum of the \(6\) faces. So, the total number of bricks that can be painted will be given by the ratio of total area of container divided by the surface area of per brick.

What is the known?

Dimensions of brick. The area can be painted with the paint.

What is the unknown?

Number of bricks can be painted.

Steps:

For a brick:

\[\begin{align} &\text {l = 22.5 cm}\\&\text{b = 10 cm}\\&\text{h = 7.5 cm}\end{align}\]

The total surface area of the brick

\[\begin{align}&={2(l b+b h+h l)} \\ &={2(22.5\!\times\!10\!+\!10\!\times\! 7.5 \!\times\!  7.5 \!\times\!  22.5)} \\ &={2(225+75+168.75)} \\ &=2(468.75) \\&= 937.5\,\mathrm{cm}^{2}\end{align}\]

Since the area given in \(\begin{align} \rm{m^2. }\end{align}\) So, the area of the brick has to be changed to \(\begin{align} \rm{m^2. }\end{align}\)

Surface area of the brick 

\[\begin{align}&= 937.5 \rm{cm^2}\\&=\frac{{937.5}}{{100 \times 100}}\rm{m^2}\\&= 0.09375\,\rm{m^2} \end{align}\]

Number of bricks can be painted 

\[\begin{align}&= \frac{{9.375}}{{0.09375}}\\ &= 100 \end{align}\]

Number of bricks that can be painted from the paint in the container \(= 100.\)

  
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