From a solid hemisphere whose radius is 2.1cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm² and also find out the cost of painting the remaining solid green at the rate of ₹1.25 per square cm.
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Answer:
The cost of the painting is 58.5 Rs
Step-by-step explanation:
Hemisphere = "r" = 2.1 cm
Means h = 2.1 cm
Now find the value of l.
l = √ (h)^2 + (r)^2
l = √ (2.1)^2 + (2.1)2
=√ 4.41 + 4.41 = √ 882/100
= √ 2 x 7 x 3 x 3 x 7 / 100
= 7 x 3 √ 2 / 10 = 21 √ 2
Since √ 2 = 1.41
= 29.64/10 = 2.964
l = 2.964 cm
Now
TSA . CSA (of hemisphere + cone)
= 2π r^2 + π rl
= π r ( 2r + l) = 22/7 x 21/10 (4.2 + 2.9)
= 66/10 x 7.1 = 4686/10
= TSA x 46.86 cm^2 x 1.25
Cost = 58.5 Rs
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