If the volume of a right circular cone of height 30 cm is 160π cm³, find the diameter of its base.

13 cm

16 cm

8 cm

7 cm

APEDIA

RRB NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

If the volume of a right circular cone of height 30 cm is 160π cm³, find the diameter of its base.

Correct Answer

8 cm

Geometric Formula Identification: The standard mathematical formula calculating the interior volume of a right circular cone is V = (1/3) * π * r2 * h, where......

💡 Analysis & Explanation

Geometric Formula Identification ▼

The standard mathematical formula calculating the interior volume of a right circular cone is V = (1/3) * π * r2 * h, where 'r' signifies the base radius and 'h' signifies the vertical height.

Data Substitution & Isolation ▼

We are given V = 160π and h = 30. Inserting these values into the formula yields: 160π = (1/3) * π * r2 * 30. We systematically divide both sides by π to eliminate the constant, leaving 160 = 10 * r2.

Solving for Dimensions ▼

Dividing by 10 gives r2 = 16. Taking the absolute square root reveals the radius r = 4 cm. Since the question asks for the diameter (which is strictly twice the radius), we multiply by 2: 4 * 2 = 8 cm.

Conclusion ▼

The diameter of the cone's base is precisely 8 cm.

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If the volume of a right circular cone of height 30 cm is 160π cm3, find the diameter of its base.

If the volume of a right circular cone of height 30 cm is 160π cm³, find the diameter of its base.