Mensuration

The volume of a sphere is given by: The total volume of the three spheres is: The volume of the new sphere is: Equating the total volume and solving for : Thus, the correct answer is 6 cm.

The volume of the cuboid is: The volume of each cube is: The number of cubes is: Thus, the correct answer is .

Let the breadth be cm. Then the length is cm. The perimeter of a rectangle is given by: Substitute the values: Thus, the length is cm and the breadth is 13 cm.

The area of the verandah is given as 90 m , and the room is of length 15 m and breadth 12 m. Let the width of the verandah be meters. The dimensions of the outer rectangle (room + verandah) are and . The area of the outer rectangle is: The area of the room is m . The area of the verandah is the difference between the area of the outer rectangle and the area of the room: Simplifying this equation: Expanding and solving: Dividing by 2: Using the quadratic formula: Thus, or (which is not possible). Therefore, the width of the verandah is m.