SURFACE AREA AND VOLUME
EXERCISE 13.9
EXERCISE 13.9
Q 1. A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the figure). The thickness of the plank is 5 cm every-where. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 poise per cm2 and the rate of painting is 10 poise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
Solution: Here, Height = 110 cm
Depth = 25 cm
Breadth = 85 cm
Thickness of the plank = 5 cm
Cost of polishing
Area to be polished = [(110 × 85)] + [(85 × 25) × 2] + [(110 × 25) × 2] +[(5 × 110) × 2] + [(75 × 5) × 4] cm2
= [9350] + [4250] + [5500] + [1100] + [1500] cm2 = 21700 cm2
Cost of polishing at the rate 20 poise per cm2
Cost of painting
∵Area to be painted = [(75 × 20) × 6] + [(90 × 20) × 2] + [90 × 75] cm2
= [9000 + 3600 + 6750] cm2
= 19350 cm2
∴Cost of painting at the rate of 10 paise per cm2
Total expenses = (Cost of polishing) + (Cost of painting)
= Rs. 4340 + Rs.1935
= Rs. 6275
Thus, the total required expense = Rs. 6275.
Q 2. The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig. 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’ and black paint costs 5 paise per cm2.
Solution: For spherical part
Surface area of a sphere = 4πr2
Surface area of a wooden sphere to be painted silver = [1386 – 7.071] cm2
= 1378.93 cm2
⇒Surface area of 8 wood spheres to be painted = 8 × 1378.93 cm2
= 11031.44 cm2
Now, the cost of silver painting at the rate of 25 paise per cm2
For cylindrical part
Radius of the base of the cylindrical part (R) = 1.5 cm
Height of the cylindrical part (h) = 7 cm
∴ Curved surface area of the cylindrical part (pillar) = 2πRh
⇒ Total curve surface area of 8 pillars = 8 × 66 cm2 = 528 cm2
∴ Cost of painting black for 8 pillars at the rate of 5 paise per cm2
Total cost of painting = [Cost of silver painting] + [Cost of black painting]
= Rs. 2757.86 + Rs. 26.40
= Rs. 2784.26
Solution: Let the original diameter = d
Per cent decrease in surface area
Decrease in curved surface area = [Original surface area] – [Decreased surface area]