Question

Assertion: A closed tank containing some water measures 9 cm by 5 cm by 6 cm. When it is placed with base 6 cm by 5 cm on the height of water in the tank is 3 cm. But when placed on the larger base 9 cm by 5 cm. The height of water is 2 cm.

Reason: Volume of water inside the tank remains the same = Area of base × height of water.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

We are given a closed tank with dimensions:

9 cm by 5 cm by 6 cm 

When the tank is placed with the base 6 cm × 5 cm, the height of water is 3 cm. When placed on the larger base 9 cm × 5 cm, the height of water is 2 cm.

This suggests that the volume of water remains the same regardless of how the tank is placed. The volume of water remains constant.

Let’s check if this is consistent: 

• Volume of water when the tank is placed on the base 6 cm × 5 cm: Volume = Area of base × Height of water = (6 × 5) × 3 = 90 cm³
• Volume of water when the tank is placed on the base 9 cm × 5 cm: Volume = Area of base x Height of water = (9 × 5) × 2 = 90 cm³

The volume of water remains the same in both cases, which supports the Assertion.

Thus, Assertion is true.

Reason (R):

The reason states that the volume of water inside the tank is the product of the area of the base and the height of the water.

This is the correct formula for calculating the volume of a rectangular container (such as a tank) filled with water. The volume is simply the area of the base multiplied by the height of the water. 

Thus, the Reason is true.