17. A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively. Find the sur- face area of the toy. (Take it = 3.14)
Answers
Step-by-step explanation:
Given :-
A toy is in the form of a cone mounted on a hemisphere.
The diameter of the base and the height of the cone are 6 cm and 4 cm respectively.
To find :-
The surface area of the toy.
Solution :-
Given that
The diameter of the base of the cone
(d) = 6 cm
We know that
Radius = Diameter / 2
Radius of the cone (r) = 6/2 = 3 cm
Radius of the cone (r) = 3 cm
=> Radius of the hemisphere = 3 cm
Height of the cone (h) = 4 cm
We know that
Slant height of a cone (l) = √(r²+h²) units
Slant height of the cone
=> l = √(3²+4²) cm
=> l = √(9+16) cm
=> l = √25 cm
=> l = 5 cm
Slant height of the given cone (l) = 5 cm
We know that
Curved Surface Area of a cone
= πrl sq.units
Curved Surface Area of the cone
=> CSA = 3.14×3×5 cm²
=> CSA = 47.1 cm²
Curved Surface Area of the cone
= 47.1 cm²
We know that
Curved Surface Area of a hemisphere
= 2πr² sq. units
Curved Surface Area of the hemisphere
= 2×3.14×3² cm²
= 2×3.14×9 cm²
= 56.52 cm²
Curved Surface Area of the hemisphere = 56.52 cm²
Now,
Surface Area of the given toy
= CSA of the cone + CSA of the hemisphere
= 47.1 cm² + 56.52 cm²
= 103.62 cm²
Answer :-
The surface area of the given toy is 103.62 cm²
Used formulae:-
→ Radius = Diameter/2
→ Slant height of a cone (l) = √(r²+h²) units
→ Curved Surface Area of a cone = πrl sq.units
→ Curved Surface Area of a hemisphere = 2πr² sq.units
- d = diameter
- r = radius
- h = height
- l = Slant height
- π = 22/7 = 3.14
Answer:
Step-by-step explanation: