# Ex.13.9 Q1 Surface Areas and Volumes Solution - NCERT Maths Class 9

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## Question

A wooden bookshelf has external dimensions as follows: Height $$= 110\rm\, cm,$$ Depth $$= 25\rm\,cm,$$ Breadth $$= 85 \rm\,cm$$ (see Fig. $$13.31$$). The thickness of the plank is $$5\rm\, cm$$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $$20$$ paise per \begin{align}\rm\,c{m^2} \end{align} and the rate of painting is $$10$$ paise per \begin{align}\rm\,c{m^2} \end{align}. Find the total expenses required for polishing and painting the surface of the bookshelf.

## Text Solution

Reasoning:

Dimensions of the cupboard and thickness wood.

What is  known?

Rate for polishing and painting.

What is  unknown?

Total expenses for painting and polishing

Steps:

length $$(l)=25 \rm\,cm$$

breadth $$(b)=85 \rm\,{cm}$$

height $$(h)=110 \rm\,{cm}$$

Surface area to be polished

\begin{align} & =\left[ \begin{array} & \left( h\times b \right)+2\left( h\times l \right)+2\left( b\times l \right)+ \\ \,2\left( h\times 5 \right)+4\left( 75\times 5 \right) \\ \end{array} \right] \\ & =\left[ \begin{array} & \left( 110\times 85 \right)+2\left( 110\times 25 \right)+ \\ 2\left( 85\times 25 \right)+2\left( 110\,\times 25 \right)+ \\ 4\left( 75\times 5 \right) \\ \end{array} \right] \\ & =\left( \begin{array} 9350+5500+4250+ \\ 1100+1500 \\ \end{array} \right)\,c{{m}^{2}} \\ & =21700\,c{{m}^{2}} \\ \end{align}

Expense required for polishing at the rate of $$20$$ paise per $$\rm\, cm^2$$

$$\therefore$$ Total expense

\begin{align}&=\frac{21700 \times 20}{100} \\ &=\operatorname{Rs} 4340 \end{align}

Surface area to be painted

\begin{align} & =\left[ \begin{array}2(20\times 90)+6(75\times 20)+ \\ (75\times 90) \\ \end{array} \right] \\ & =(3600+9000+6750)c{{m}^{2}} \\ & =19350\text{c}{{\text{m}}^{2}} \\ \end{align}

At the rate of $$10$$ paise per $$\rm sq. cm = 1935$$

Expense required for polishing and painting the surface of the bookshelf.

$$= 4340 + 1935 = 6275$$

Total expense required for polishing and painting the surface of the bookshelf $$= 6275.$$