"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 the given 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 .
Class 9 - Math - Surface Areas and Volumes Page 237"
Answers
Given: R= 21/2 cm , r= 1.5 cm, h=7cm
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 paint= 8(curved surface area of the sphere – area of circle on which sphere is resting)
= 8(4πR² - πr²)
= 8π(4R² - r²)
= 8π{4×(21/2)² -(1.5)²}
=8π(4× 441/4- 2.25)
= 8π(438.75) cm²
Therefore the cost of paint @ 25 paise per cm²
=( 8× 22/7 × 438.75× 25/100)
= 19305/7= ₹ 2757.86 (approx)
Hence, surface area to be painted black = 8 × curved surface area of cylinder
= 8 × 2πrh
= 8×2×22/7×1.5×7
= 528 cm²
Cost of black paint @ 5 Paise per cm²= (528×5/100)= 528/20
=₹ 26.40
total cost of painting=
₹ 2757.86+26.40
= ₹ 2784.26(approx)
Hence, total cost of painting= ₹ 2784.26(approx)
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Hope this will help you....
