Question
A right circular cone has a base
area of 154 cm² and a slant height of 25 cm. What is the volume of the cone?Solution
ATQ,
The base area of the cone is given by the formula: π × radius² So, π × (radius of the cone)² = 154 Thus, (radius of the cone)² = 154 × (7/22) = 49 This means the radius of the cone = √49 = 7 cm We know that (slant height)² = (radius)² + (height)² Therefore, (height)² = 25² – 7² = 625 – 49 = 576 So, the height of the cone = √576 = 24 cm Now, the volume of the cone = (1/3) × π × radius² × height = (1/3) × (22/7) × 49 × 24 = 1232 cm³
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