C and C2 are two cylinders having equal total surface areas. The radius of each
cylinder is equal to the height of the other. The sum of the volumes of both the
cylinders is 250pi cm^2. Find the sum of their curved surface areas.
PLEASE ANSWER IN CORRECT WORDS.
Answers
Let A be the surface area of two cylinders (C1 and C2) having heights and radii h₁, r₁ and h₂, r₂ respectively.
The radius of each cylinder is equal to the height of the other.
r₁ = h₂ and r₂=h₁
Volume of C1 = πr₁²h₁ = π h₂²h₁
Volume of C2 = πr₂²h₂ = π h₁²h₂
Sum of volumes = π h₂²h₁+ π h₁²h₂
250π = π(h₂²h₁+ h₁²h₂)
250 = h₁h₂(h₂+h₁) —-(1)
Curved surface area of C1 = 2πr₁h₁ = 2πh₁h₂
Total surface area of C1 =2πh₁h₂+ 2πr₁²= 2πh₁h₂+ 2πh₂²
Curved surface area of C2 = 2πr₂h₂ = 2πh₁h₂
Total surface area of C2 =2πh₁h₂+ 2πr₂²= 2πh₁h₂+ 2πh₁²
Both total surface areas are equal.
2πh₁h₂+ 2πh₂² =2πh₁h₂+ 2πh₁²
h₂² =h₁²
h₁=h₂
From (1), 250 = h₁h₁(2h₁) = 2h₁³
h₁³ =125
h₁=h₂=5
Sum of curved surface area = 2π(5)(5)+2π(5)(5) = 100π
Ans: 100π:
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Step-by-step explanation:
Let A be the surface area of two cylinders (C1 and C2) having heights and radii h₁, r₁ and h₂, r₂ respectively.
The radius of each cylinder is equal to the height of the other.
r₁ = h₂ and r₂=h₁
Volume of C1 = πr₁²h₁ = π h₂²h₁
Volume of C2 = πr₂²h₂ = π h₁²h₂
Sum of volumes = π h₂²h₁+ π h₁²h₂
250π = π(h₂²h₁+ h₁²h₂)
250 = h₁h₂(h₂+h₁) —-(1)
Curved surface area of C1 = 2πr₁h₁ = 2πh₁h₂
Total surface area of C1 =2πh₁h₂+ 2πr₁²= 2πh₁h₂+ 2πh₂²
Curved surface area of C2 = 2πr₂h₂ = 2πh₁h₂
Total surface area of C2 =2πh₁h₂+ 2πr₂²= 2πh₁h₂+ 2πh₁²
Both total surface areas are equal.
2πh₁h₂+ 2πh₂² =2πh₁h₂+ 2πh₁²
h₂² =h₁²
h₁=h₂
From (1), 250 = h₁h₁(2h₁) = 2h₁³
h₁³ =125
h₁=h₂=5
Sum of curved surface area = 2π(5)(5)+2π(5)(5) = 100π
Ans: 100π:
HOPE IT HELPED! FOLLOW AND MARK AS BRAINLIEST!