A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of hemisphere. If the radius of base of the cone is 21cm and the volume is 
of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy (Use 
).
Answers
Answer:
The height of the cone is 28 cm and the surface area of a toy is 5082 cm² .
Step-by-step explanation:
SOLUTION :
Given :
Radius of cone = Radius of hemisphere, r = 21 cm
Volume of cone = 2/3 Volume of hemisphere
⅓ πr²h = ⅔ × ⅔ ×πr³
⅓ r²h = 4/9 ×r³
⅓ × 21² × h = 4/9 × 21³
h = (3 × 4 × 21³)/(9 × 21²)
h = (4 × 21)/3 = 4 × 7 = 28 cm
h = 28 cm
Hence, the height of the cone is 28 cm .
Slant height , l = √(h² + r²)
l = √(28² + 21²)
l = √(784 + 441)
l = √(1225)
l = 35 cm
Curved surface area of a toy ,S = Curved surface area of hemisphere + curved surface area of cone
S = 2πr² + πrl
S = πr(2r + l)
S = 22/7 × 21 (2 × 21 + 35)
S = 66 × (42 + 35)
S = 66 × 77
S = 5082 cm²
Hence, the height of the cone is 28 cm and the surface area of a toy is 5082 cm²
HOPE THIS ANSWER WILL HELP YOU...
The height of the cone is 28 cm
and
surface area of the toy is 5082 cm²
Step-by-step explanation:
Given,
Radius of cone = Radius of hemisphere, r = 21 cm
Volume of cone = 2/3 Volume of hemisphere
=> ⅓ πr²h = ⅔ × ⅔ ×πr³
=> ⅓ r²h = 4/9 ×r³
putting the value of 'r'
we get,
=> ⅓ × 21² × h = 4/9 × 21³
=> h = (3 × 4 × 21³)/(9 × 21²)
=> h = (4 × 21)/3 = 4 × 7 = 28 cm
=> h = 28 cm
Hence,
the height of the cone is 28 cm .
therefore,
Slant height , l = √(h² + r²)
=> l = √(28² + 21²)
=> l = √(784 + 441)
=> l = √(1225)
=> l = 35 cm
also,
Curved surface area of a toy ,S = Curved surface area of hemisphere + curved surface area of cone
=> S = 2πr² + πrl
=> S = πr(2r + l)
=> S = 22/7 × 21 (2 × 21 + 35)
=> S = 66 × (42 + 35)
=> S = 66 × 77
=> S = 5082 cm²
Hence,
the height of the cone is 28 cm
and
the surface area of a toy is 5082 cm²