A toy is in the form of a cone of radius 3.5 cm mounted on a hrmisphere of same radius .The total height of the toy is 15.5 cm. find the total surface area of the toy
Answers
Answer:
Total surface area of toy = Curved surface area of cone + surface area of hemisphere
Curved surface area of cone = πrl
Where r=3.5cm, Height =15.5−3.5=12cm
And hence, l=12.5cm (by using formula l2=h2+b2)
Therefore C.S.A. of cone =π×3.5×12.5
=137.5cm2
Surface area of hemisphere =2πr2
=2×π×(3.5)2
=77cm2
Hence T.S.A of toy =77+137.5=214.5cm2
Answer:
We have,
Radius of cone = Radius of hemisphere = 3.5 cm.
Height of the toy = 15.5 cm
To calculate the CSA of cone we have to find first the Slant Height of the cone :]
Slant Height = h² + r²
Slant Height = (15.5)² + (3.5)²
Slant Height = 12.25 + 144
Slant Height = 156.25 cm²
Slant Height = 12.5 cm
Now, we will calculate the TSA of the toy :
➳ TSA of toy = CSA of hemisphere + CSA of cone
➳ TSA of toy = 2πr² + πrl
➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)
➳ TSA of toy = 24.5π + 43.75π
➳ TSA of toy = 68.25π
➳ TSA of toy = 68.25 * 22/7
➳ TSA of toy = 214.5 cm²