Question
Quantity I: A sphere has a total
surface area of 2464 m². Calculate the sphere’s volume. Quantity II: For a cone, the sum of its radius and height is 28 m, and the ratio of the radius to the height is 11:3. Determine the cone’s volume. Quantity III: The side of a cube and the length of a cuboid are in the ratio 2:5. The cube has a volume of 64 m³. Furthermore, the ratios of the length to breadth and length to height of the cuboid are 5:3 and 5:7, respectively. Find the cuboid’s volume. For every question, evaluate the three provided quantities, compute their respective values, and analyze how they compare to each other.Solution
ATQ, Quantity I: So, 4×22/7×r×r = 2464, r = 14m So, the volume is 22/7×14×14×14×4/3 = 11498.66 m Quantity II: Radius is 28×11/14 = 22m, height is 28 - 22 = 6m So, volume is =1/3×22/7×22×22×6 = 3042.28m Quantity III: The side of the cube is 4m So, the length of the cuboid is 4×5/2 = 10m The breadth of the cuboid is 10×3/5 = 6m The height of the cuboid is 10×7/5 = 14m So, volume is 10×6×14 = 840m Quantity I > Quantity II > Quantity III
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