Ex 12.1, 3 - Chapter 12 Class 10 Surface Areas and Volumes

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 12.1, 3
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Total surface area of toy
= Curved Surface area of hemisphere
+ Curved Surface area of cone
Curved Surface area of hemisphere
Radius of hemisphere = Radius of cone = r = 3.5 cm
Curved surface area of hemisphere = 2šš2
= 2 Ć22/7Ć (3.5)2
= 2 Ć22/7Ć (3.5)2
= 2 Ć22/7Ć 3.5 Ć 3.5
= 2 Ć 22 Ć 0.5 Ć 3.5
= 77 cm2
Curved surface area of cone
Curved surface area of cone = š šš
Radius of cone = r = 3.5 cm
Height of cone = Total height of toy ā radius of hemisphere
= 15.5 ā 3.5
= 12 cm
Now, we find slant height (l)
We know that
l2 = h2 + r2
l2 = (12)2 + (3.5)2
l2 = (12)2 + (7/2)^2
l2 = 144 + 49/4
l2 = (144(4) + 49)/4
l2 = (576 + 49)/4
l2 = ššš/š
l = ā(625/4)
l = ā(25^2/2^2 )
l = šš/š
l = 12.5 cm
Curved surface area of cone = Ļrš
= 22/7 Ć 3.5 Ć 12.5
= 22 Ć 0.5 Ć 12.5
= 137.5 cm2
Now,
Total surface area of toy
= Curved Surface Area of hemisphere
+ Curved Surface Area of cone
= 77 + 137.5
= 214.5 cm2
Hence, total surface area of the toy is 214.5 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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