Question
Which of the following is the correct relation between
Quantity I and Quantity II? Quantity I: A cylindrical tank has a radius of 10 cm and a height of 20 cm. Find the total surface area of the tank. Quantity II: A conical tank has a radius of 10 cm and a height of 20 cm. Find the total surface area of the tank.Solution
Quantity I: Surface area of a cylinder = 2πr(h + r) = 2π × 10 × (20 + 10) = 2π × 10 × 30 = 600π cm² Quantity II: Surface area of a cone = πr(l + r), where l is the slant height Slant height, l = √(r² + h²) = √(10² + 20²) = √100 + 400 = √500 ≈ 22.36 cm Surface area = π × 10 × (22.36 + 10) = π × 10 × 32.36 ≈ 323.6π cm² Comparing Quantity I and Quantity II: Quantity I = 600π cm² Quantity II ≈ 323.6π cm² Now, comparing: Quantity I > Quantity II Therefore, the correct option is: B
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