The radius of a solid hemisphere is 7 centimetres. Find the volume of the hemisphere in cubic centimetres.

Introduction / Context:
This numerical problem involves the volume of a solid hemisphere. Hemispheres are half spheres and appear in questions related to containers, domes, and various real life shapes. Knowing the formula for the volume of a hemisphere is important for geometry and mensuration.

Given Data / Assumptions:

• The solid is a hemisphere.
• Radius r = 7 cm.
• We are asked to find the volume in cubic centimetres.
• Use the standard value of pi as 22 / 7 for calculation.

Concept / Approach:
Volume of a sphere of radius r is:
V_sphere = (4 / 3) * pi * r^3.
A hemisphere is half of a sphere, so:
V_hemisphere = (1 / 2) * V_sphere = (2 / 3) * pi * r^3.
We substitute r = 7 cm and pi = 22 / 7 into this formula to find the answer.

Step-by-Step Solution:
Step 1: Write the volume formula for a hemisphere: V = (2 / 3) * pi * r^3. Step 2: Substitute r = 7 cm and pi = 22 / 7. Step 3: Compute r^3: 7^3 = 7 * 7 * 7 = 343. Step 4: Substitute values: V = (2 / 3) * (22 / 7) * 343. Step 5: Simplify (22 / 7) * 343 = 22 * 49 = 1078. Step 6: Now V = (2 / 3) * 1078. Step 7: Compute 2 * 1078 = 2156, then divide by 3 to get approximately 718.67 cubic centimetres.

Verification / Alternative check:
Another way is to first compute the volume of the full sphere with radius 7 cm, then divide by 2. Sphere volume = (4 / 3) * pi * 7^3. Using pi = 22 / 7 gives approximately 1437.34 cubic centimetres. Half of this is 1437.34 / 2 = 718.67 cubic centimetres, which matches the previous result.

Why Other Options Are Wrong:
1437.34 cubic centimetres: This is the volume of the full sphere, not the hemisphere.
239.56 cubic centimetres and 359.34 cubic centimetres: These are much smaller than half the sphere volume and result from incorrect application of the formula.
500 cubic centimetres: A rounded guess, not supported by proper computation and significantly off from the correct value.

Common Pitfalls:
A common mistake is to forget to take half of the sphere volume for a hemisphere, or to use the formula for a sphere directly. Some also incorrectly cube the radius or simplify fractions wrongly, especially when pi is taken as 22 / 7. Carefully substituting and simplifying step by step avoids these errors.

Final Answer:
The volume of the hemisphere is approximately 718.67 cubic centimetres.