A man has solids of shapes (sphere, cube, cylinder, cuboid & cone) Area of base of cuboid is 110 cm². Radius of sphere and cylinder are equal but volume of cylinder is 25% less than the volume of sphere. Height of cone is equal to the edge of cube and volume of cube of volume of cone. Radius cone is equal to height of cuboid and height of cuboid is half of the diameter of the sphere. Ratio of volume of cylinder, cuboid and cube are 462 : 110 : 441 respectively. Q. Surface area of cube is what % of the total surface area of cylinder ?
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Surface area of cube is 50 % of the total surface area of cylinder
Step-by-step explanation:
Area of base of cuboid is 110 cm²
let say height = h₁
then Volume = 110h₁
Radius of sphere and cylinder are equal but volume of cylinder is 25% less than the volume of sphere.
=> Volume of Sphere = (4/3)π R₁³
Volume of cylinder = π R₁²h₂
π R₁²h₂ = (3/4) (4/3)π R₁³
=> h₂ = R₁
height of cuboid is half of the diameter of the sphere.
=> h₁ = h₂ = R₁
Height of cone is equal to the edge of cube and volume of cube of volume of cone
= > (1/3)πr₂²h₃ = h₃³
Radius cone is equal to height of cuboid
=> πh₁²h₃ / 3 = h₃³
=> πh₁² = 3 h₃²
Surface area of cube = 6h₃²
surface area of cylinder = 2πR₁² + 2πR₁h₁ = 4πh₁² = 4 * 3 h₃² = 12h₃²
Surface area of cube is 50 % of the total surface area of cylinder
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