A toy is in the form a cone of radius 3.5 cm mounted on a hemisphere of same radius the total height of the toy is 15.5cm . find the total surface area of the toy
Answers
Answer:
rad.of cone =rad.of hemisphere=3.5 cm (given)
Also,
height of toy=15.5 cm (given)
height of hemisphere=3.5 cm
height of cone=15.5-3.5
=12cm
slant height . of cone=under root h^2+r^2
=under root (12^2+3.5^2)
=under root 144+12.25
=under root 156.25
= 12.5 cm
CSA oc hemisphere=2×22/7×(3.5)^2
=77 cm^2
CSA of cone=22/7×3.5×12.5
=137.5 cm^2
TSA of toy=CSA of hemisphere+CSA of cone
=77+137.5
=214.5cm^2
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