Question

ABC Corporation needs at least 400 kilolitres of water in its factory at all times. It considers a spherical tank with uniform wall thickness. The outer diameter of the tank is 10 m. Is the tank capacity adequate?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weighs 30,000 kg when empty, and is made of material with density 3 g/cc.

• A. if the question can be answered using A alone but not B alone.
• B. if the question can be answered using B alone but not A alone.
• C. if the question can be answered using A and B together, but not using either A or B alone.
• D. if the question cannot be answered even using A and B together.

Hint:

For capacity questions, knowing the inner dimensions of the container is enough to calculate volume directly.

Answer 1

The Correct Option is A

To determine if the spherical tank has enough capacity, we must calculate its volume and check if it meets the requirement of at least 400 kilolitres (or 400,000 litres). The volume \(V\) of a sphere is calculated using the formula: \(V = \frac{4}{3}\pi r^3\), where \(r\) is the radius.

Let's evaluate each statement:

Statement A 

The inner diameter of the tank is at least 8 meters. Thus, the inner radius \(r\) is at least 4 meters.

Substituting into the volume formula:

\(V = \frac{4}{3}\pi (4)^3\)

\(V = \frac{4}{3}\pi (64)\)

\(V = \frac{256}{3}\pi\) cubic meters

\(\approx 268.08\) cubic meters

Since 1 cubic meter is equivalent to 1 kilolitre, the tank can hold approximately 268.08 kilolitres. This is insufficient, as it is less than 400 kilolitres. Therefore, Statement A alone tells us the capacity is inadequate.

Statement B

The weight of the empty tank is 30,000 kg, with the material's density being 3 g/cc, or 3000 kg/m³.

Using density, we calculate the volume of material used in the tank:

\(Volume = \frac{Mass}{Density}\)

\(Volume = \frac{30000}{3000} = 10\) cubic meters

This volume is the difference between the outer and inner volumes of the tank. However, without the inner diameter or radius, we cannot determine the inner volume or the capacity. Therefore, Statement B alone is insufficient.

Conclusion

Statement A alone provides enough information to determine the tank's capacity is inadequate by itself, while Statement B alone does not provide sufficient information. Thus, the correct choice is if the question can be answered using A alone but not B alone.