Find the volume, in cubic centimetres, of a solid sphere whose diameter is 7 centimetres.

Introduction / Context:
This question tests your knowledge of the volume formula for a sphere and the ability to use the given diameter to first find the radius. Spherical shapes are common in mensuration problems related to geometry, physics, and everyday objects.

Given Data / Assumptions:

• The solid is a sphere.
• Diameter d = 7 cm.
• Radius r = d / 2.
• We need the volume in cubic centimetres.
• Take pi = 22 / 7 for calculation.

Concept / Approach:
The volume of a sphere is given by:
V = (4 / 3) * pi * r^3.
We must first compute the radius as half the diameter, then cube the radius, and substitute into the formula with pi = 22 / 7.

Step-by-Step Solution:
Step 1: Diameter d = 7 cm, so radius r = d / 2 = 7 / 2 = 3.5 cm. Step 2: Use the formula V = (4 / 3) * pi * r^3. Step 3: Substitute r = 3.5 and pi = 22 / 7. Step 4: Compute r^3: 3.5 * 3.5 * 3.5 = 42.875. Step 5: So V = (4 / 3) * (22 / 7) * 42.875. Step 6: Combine constants: (4 / 3) * (22 / 7) * 42.875. Step 7: Using an exact fraction approach, 3.5^3 = 42.875, and simplifying gives approximately 179.67 cubic centimetres.

Verification / Alternative check:
We can approximate using 3.14 for pi to confirm. Then:
V ≈ (4 / 3) * 3.14 * 3.5^3 ≈ 1.333 * 3.14 * 42.875.
1.333 * 3.14 ≈ 4.185, and 4.185 * 42.875 ≈ 179.5 cubic centimetres, close to 179.67 cubic centimetres. Both approximations are consistent and validate the answer.

Why Other Options Are Wrong:
140.25 cubic centimetres: This is significantly lower than the correct volume and results from incorrect multiplication or using radius directly without cubing.
213.74 cubic centimetres and 337.16 cubic centimetres: These are larger than the correct volume and come from overestimation or misusing the formula.
250 cubic centimetres: A rounded guess that does not match exact calculations.

Common Pitfalls:
Common errors include using the diameter instead of the radius in the formula, failing to cube the radius, or using an incorrect formula such as 4 * pi * r^2, which is for surface area, not volume. Careful attention to the formula and proper identification of radius versus diameter are essential.

Final Answer:
The volume of the sphere is approximately 179.67 cubic centimetres.