hey there please answer legends
answer is 18√2π sq. units
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Solution :
i ) Let the radius of smaller cone =r
height = h
Volume ( V ) = 12π
=> ( πr²h )/3 = 12π
πrl = 15π
=> r√(r² + h² ) = 15
{ Since , l = √r² + h² }
Squaring both sides , we get
=> r² ( r² + h² ) = 15 × 15
= 3×5×3×5
= 3×3×25
=> r²(r²+h²) = 3²( 3²+4²)
compare both sides,
r = 3 , h = 4
CSA = π × 3 × √(3²+4²) = 15π
ii ) Now ,
radius of the Larger cone = r
height = H
volume = (πr²H)/3 = 96π
=> ( r²H)/3=96
=> ( 3×3×H)/3= 96
=> 3H = 96
=> H = 96/3
=> H = 32
l = √(r² + H² )
= √( 3² + 32² )
= √ 9+1024
= √1033
CSA = πrl
= π × 3 ×√1033
••••
i ) Let the radius of smaller cone =r
height = h
Volume ( V ) = 12π
=> ( πr²h )/3 = 12π
πrl = 15π
=> r√(r² + h² ) = 15
{ Since , l = √r² + h² }
Squaring both sides , we get
=> r² ( r² + h² ) = 15 × 15
= 3×5×3×5
= 3×3×25
=> r²(r²+h²) = 3²( 3²+4²)
compare both sides,
r = 3 , h = 4
CSA = π × 3 × √(3²+4²) = 15π
ii ) Now ,
radius of the Larger cone = r
height = H
volume = (πr²H)/3 = 96π
=> ( r²H)/3=96
=> ( 3×3×H)/3= 96
=> 3H = 96
=> H = 96/3
=> H = 32
l = √(r² + H² )
= √( 3² + 32² )
= √ 9+1024
= √1033
CSA = πrl
= π × 3 ×√1033
••••
Answered by
1
Answer:
60π unit²
Step-by-step explanation:
Find the scale factor:
(length1/length2)³ = volume1/volume2
(length1/length2)³ = 12π/96π
(length1/length2)³ = 1/8
length1/length2 = ∛(1/8)
length1/length2 = 1/2
The scale factor is 1/2
Find the curved surface area of the larger cone:
area1/area2 = (length1/length2)²
15π/area2 = (1/2)²
15π/area2 = 1/4
area2 = 4 x 15π
area2 = 60π unit²
Answer: 60π unit²
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