Final answer:
To calculate the volume of a right circular cone with a height of 13.4 m and a base radius of 12.5 m, use the cone volume formula V = (1/3)πr²h. The calculated volume is approximately 21984.9 m³ when rounded to the nearest tenth.
Step-by-step explanation:
To find the volume of a right circular cone with a height of 13.4 m and a base radius of 12.5 m, we can use the formula for the volume of a cone, which is V = (1/3)πr²h. In this formula, π (pi) is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone. Plugging in our values, we get:
V = (1/3)(3.14159)(12.5 m)²(13.4 m)
Calculating this, we have:
V ≈ (1/3)(3.14159)(156.25 m²)(13.4 m) ≈ (1/3)(3.14159)(2093.75 m³)
V ≈ 21984.9 m³
When rounding to the nearest tenth, the volume of the cone is approximately 21984.9 m³.