Volume of cylindrical pillar (material used): A solid circular pillar has diameter 14 cm (radius 7 cm) and height 5 m (i.e., 500 cm). Assuming it is a solid cylinder, find its volume in cm^3.

Introduction / Context:
The volume of a solid cylindrical pillar is V = πr^2h. Dimensions are given with mixed units (cm and m), so convert consistently before computation. Present the exact result using π = 22/7 to get a neat factorization in the provided format.

Given Data / Assumptions:

• Diameter = 14 cm → r = 7 cm
• Height h = 5 m = 500 cm
• V = πr^2h

Concept / Approach:
Keep units in centimeters to match the requested cm^3 output. Using π = 22/7 typically simplifies multiples involving 7 in r.

Step-by-Step Solution:
V = π * 7^2 * 500 = π * 49 * 500 = 24500π cm^3With π = 22/7 → V = 24500 * (22/7) = 3500 * 22 = 77000 cm^3Expressed as 77 × 10^3 cm^3

Verification / Alternative check:
Rough check with π ≈ 3.14: 24500π ≈ 76930 cm^3, consistent with 77000 when π = 22/7 is used by design.

Why Other Options Are Wrong:
(77 × 10^2) and (77 × 10^4) are off by factors of 10; (77 × 10^5) and (77 × 10^6) are orders of magnitude too large.

Common Pitfalls:
Not converting 5 m to 500 cm; using diameter in r^2; rounding mid-calculation instead of at the end.

Final Answer:
(77 x 10^3)cm3