## Chapter 13 Surface Areas and Volumes Ex 13.9

**Question 1.** **A wooden bookshelf has external dimensions as follows : Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 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 cm ^{2} and the rate of pointing is 10 paise per cm^{2}, find the total expenses required for palishing and painting the surface of the bookshelf.**

**Solution:**

Here, l = 85 cm b = 25 cm and h = 110 cm

Area of the bookshelf of outer surface = 2 lb + 2bh + hl

= [2(85 x 25)+ 2(110 x 25)+ 85×110] cm2 = (4250 + 5500 + 9350) cm

^{2}= 19100 cm

^{2}

Cost of polishing of the outer surface of bookshelf

= 19100 x 20100 = ₹ 3820

Thickness of the plank = 5 cm

Internal height of bookshelf = (110 – 2 x 5) = 100 cm

Internal depth of bookshelf = (25 – 5) = 20 cm

Internal breadth of bookshelf = 85 – 2 x 5 = 75 cm

Hence, area of the internal surface of bookshelf

= 2(75 x 20)+ 2(100x 20)+ 75×100

= 3000 + 4000 + 7500 = 14500 cm2

So, cost of painting of internal surface of bookshelf

= 14500 x 10100 = ₹1450

Hence, total costing of polishing and painting = 3820 + 1450= ₹ 5270

**Question 2.** **The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in figure. Eight such spheres are-used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm ^{2} and black paint costs 5 paise per cm^{2}.**

**Solution:**

It is obvious, we have to subtract the cost of the sphere that is resting on the supports while calculating the cost of silver paint.

Surface area to be silver paint

**Question 3.** **The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?** **Solution:**

Let d be the diameter of the sphere