Question 14 Marks

The figure below shows a blueprint of a shower room of a club.

The walls of the shower room (inner boundary) is 0.1 m thick. The wall of outer boundary is 0.2 m thick.
On the basis of above given information, answer the following questions.
Q.1. The inside wall and the floor of the shower room are covered with tiles. What area of the shower room is covered with tiles?
(a) $20.54 m^2$ $\qquad$ (c) $57.5 m^2$
(b) $37.52 m^2$ $\qquad$ (d) $65.20 m^2$
Q.2. Which of the following calculations shows the inside volume (in $m ^3$ ) of the shower room?
(a) $79 \times 2.6 \times 1.76$ $\qquad$ (b) $7.9 \times 31 \times 1.76$
(c) $8.2 \times 3.1 \times 1.76$ $\qquad$ (d) $8.5 \times 4.2 \times 1.76$
Q.3. An area is marked for cupboards.
How many cupboards with dimensions $1.5 \times 0.6 \times 1.76$ (length $\times$ breadth $\times$ height) can be built in the area?
Q.4. One litre of paint is required to paint 12 sq m . Approximately, how many litres of paint are required to paint the outer boundary of the shower room?
(a) 3 $\qquad$ (b) 5 $\qquad$
(c) 60 $\qquad$ (d) 89

Answer

1. (c) Firstly, find the total length and breadth of shower room.
Surface area of the floor and inside wall of shower room = Surface area of floor + Surface area of inside wall
$\begin{array}{l}=l \times b+2 h(l+b) \\ =7.9 \times 2.6+2 \times 1.76 \times(7.9+2.6) \\ =20.54+36.96=57.5\end{array}$
Hence, the area of shower room covered with tiles is $57.5 m^2$
2. (a) Length of shower room excluding inner and outer boundary
$\begin{array}{l}=\text { Total length }- \text { Inner boundary }- \text { Outer boundary } \\ =8.5-2 \times 0.1-2 \times 0.2=8.5-2 \times 0.3=7.9\end{array}$
Total breadth of shower room excluding inner and outer boundary and cupboard area
$\begin{array}{l}=4.2-2 \times 0.2-2 \times 0.1-1 \\ =4.2-2 \times 0.3-1=2.6\end{array}$
Height of the shower room $=1.76$
$\therefore$ Inside volume of shower room
$=$ Length $\times$ Breadth $\times$ Height $=7.9 \times 2.6 \times 1.76$
3. Dimensions for one cupboard is $1.5 \times 0.6 \times 1.76$ (Length $\times$ Breadth $\times$ Height).
Then, the required area for one cupboard
$
=\text { Length } \times \text { Breadth }=1.5 \times 0.6=0.9 m^2
$
Length of one portion of cupboard $=3.5 m$
Breadth of one portion of cupboard $=1 m$
$\therefore$ Total area of cupboard $=35 \times 1=3.5 m$
Then, the number of cupboards in one portion
$=\frac{\text { Total area of cupboard }}{\text { Area of one cupboard }}=\frac{3.5}{0.9}=3.888$
Hence, approximately 4 cupboards can be built in the one portion of shower room and total 8 cupboards can be built in the total portion of cupboard area of shower room.
4. (a) To find the paint required to paint the outer boundary of the shower room, it need to find the surface area of outer wall.
$\therefore$ Surface area of outer wall
$
\begin{array}{l}
=h \times(L+B) \quad [ L=\text { total length, } B=\text { total breadth } ]\\
=1.76 \times[(8.5+8.5-1.5)+2 \times 4.2] \\
=1.76 \times(23.9)=35.68 m^2
\end{array}
$
Paint required for $12 m^2=1 L$
$
\text { Paint required for } \begin{aligned}
35.68 m^2 & =\frac{35.68 m^2}{12} L \\
& =2.973=3 L
\end{aligned}
$
Hence, approximately 3 L paint is needed to paint the outer walls of shower room.

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