The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig 13.32. 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 cm2 and black paint costs 5 paise per cm2.
Solution:
Since each sphere is placed on the cylinder, the area which is to be painted silver will be calculated by subtracting the top circular area of the cylinder from the surface area of the sphere.
The area of the cylinder which is to be painted black is the CSA of the cylinder.
The surface area of a sphere = 4πr2
CSA of the cylinder = 2πrh
Diameter of the wooden sphere = 21cm
The radius (R) of the wooden sphere = 21/2 cm
Surface area for wooden sphere = 4πR2
= 4 × 22/7 × 21/2 cm × 21/2 cm
= 1386 cm2
Since the support is a cylinder of radius, r = 1.5 cm
Area of the circular end of the cylinder = πr2
= 22/7 × 1.5 cm × 1.5 cm
= 7.07 cm2
So, the area of each wooden sphere to be painted = 1386 cm2 - 7.07 cm2 = 1378.93 cm2
Total area of the 8 spheres to be painted = 8 × 1378.93 cm2 = 11031.44 cm2
Cost of silver painting the wooden spheres at the rate of 25 paise per cm2
= 11031.44 × ₹ (25/100)
= ₹ 2757.86
Now,
Radius of the cylinder, r = 1.5 cm
Height of the cylinder, h = 7 cm
Curve surface area of the cylinder = 2πrh
= 2 × 22/7 × 1.5 cm × 7 cm
= 66 cm2
CSA of 8 cylindrical support to be painted = 8 × 66 cm2 = 528 cm2
Cost of black painting the cylindrical support at 5 paise per cm2
= 528 × ₹ (5/100)
= ₹ 26.40
Hence the cost of paint required = ₹ 2757.86 + ₹ 26.40
= ₹ 2784.26
Thus, the cost of paint required is ₹ 2784.26 (approx.)
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Fig 13.32. 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 cm² and black paint costs 5 paise per cm².
NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.9 Question 2
Summary:
It is given that the front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports of cylinders with radius 1.5 cm and height 7 cm which are to be painted silver and black respectively at the rate of 25 paise per cm² and 5 paise per cm². We have found that the total cost of the paint required is ₹ 2784.26.
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