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

## Question

**Q1.** 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 \((h)=110 \rm\,{cm}\)

\(\begin{align}\text{Surface area to be polished} \\&=(h×b)+2(h×l)+2(b×l)+2(h×5)+4(75×5)\\&=(110×85)+2(110×25)+2(85×25)+2(110×25)+4(75×5)\\&=(9350+5500+4250+1100+1500) cm^2\\&=21700 \rm\,cm^2\end{align}\)

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

\[\begin{align} \therefore \text { Total expense } &=\frac{21700 \times 20}{100} \\ &=\operatorname{Rs} 4340 \end{align}\]

Surface area to be painted

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

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

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

\(= 4340 + 1935 = 6275\)

**Answer:**

Total expense required for polishing and painting the surface of the bookshelf \(= 6275.\)