Question
Quantity I: The radius of a cone is twice the radius of
a sphere, and the total surface area of the cone is 704 cm². The height of the cone is equal to the length of a rectangle, and the perimeter of the rectangle (in cm) is 66 units less than the total surface area of the sphere, which is 154 cm². What is the area of the rectangle? Quantity II: The length of a cuboid is 50% greater than the side of a cube, which has a surface area of 864 cm². The ratio of the height, length, and base of the cuboid is 4:6:3. Find 25% of the volume of the cuboid. Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give an answer.Solution
Answer: C From quantity I, SA of sphere = 4 * 22/7 * r * r 154 = 4 * 22/7 * r * r Radius of the sphere = 3.5 cm Radius of the cone = 2 * 3.5 = 7 cm SA of cone = 22/7 * r * (l + r) 704 = 22/7 * 7 * (l + 7) 32 = l + 7 l = 25 cm Height of the cone = √(252 – 72) = 24 cm Length of the rectangle = 24 cm Perimeter of the rectangle = 154 – 66 = 88 cm Breadth of the rectangle = 88/2 – 24 = 20 cm Area of the rectangle = 20 * 24 = 480 cm2 From quantity II, SA of cube = 6a2 = 864 a = 12 cm Length of the cuboid = 150/100 * 12 = 18 cm Height of the cuboid = 18 * 4/6 = 12 cm Base of cuboid = 18 * 3/6 = 9 cm Volume of the cuboid = 9 * 12 * 18 = 1944 cm3 Required Answer = 1944 * 25/100 = 486 cm3  Quantity I < quantity II
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