Question

A tank is filled with certain amount of water upto its top edge. Is the volume of tank greater than 514 m³?
Statement 1: The amount of water in the tank is 1000 litres
Statement 2: The outer surface of tank is in the form of a cube of length 10 m

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

Answer: (E)

To determine whether the volume of the tank is greater than 514 m³, let's examine the information provided in each statement:

1. Statement 1: The amount of water in the tank is 1000 litres.

First, convert the volume of water given in litres to cubic meters. We know that 1 cubic meter equals 1000 litres. Therefore, 1000 litres is equivalent to 1 cubic meter.

\[ \text{Volume in } \mathrm{m^3} = \frac{1000 \text{ litres}}{1000} = 1 \text{ m}^3 \]

From this statement alone, we know the tank can hold at least 1 m³ of water, but whether it can hold more than 514 m³ of water is not determined.

2. Statement 2: The outer surface of the tank is in the form of a cube of length 10 m.

Given that the tank is a cube with a side length of 10 meters, we can calculate its volume using the formula for the volume of a cube:

\[ \text{Volume of cube} = \text{side}^3 = 10^3 = 1000 \text{ m}^3 \]

This statement alone tells us that the outer dimensions of the tank enclose a space of 1000 m³. However, this does not directly ensure that the tank volume (inside capacity) is greater than 514 m³ without additional information on the wall thickness or inner lining constraints, if any.

Therefore, analyzing both statements separately:

• Statement 1 alone is insufficient as it only provides the current water volume.
• Statement 2 alone is insufficient as it provides only the external dimensions.

Combining both statements does not provide information that definitively answers whether the tank's volume (capacity) exceeds 514 m³ due to the possibility of internal structural features affecting volume capacity.

Hence, the correct answer is: Neither statement (1) nor statement (2) suffices to answer the question.