The volume of the first cone is 30m³. In the second cone, the base radius is 2 times the radius of the first cone

| June 21, 2021 | education

The volume of the first cone is 30m³. In the second cone, the base radius is 2 times the radius of the first cone, and the height of the second is 3 times less than the height of the first. Find the volume of the second cone. Indicate the answer in m³.

1. In trigonometry, the formula for finding the volume of a cone is known: V = 1/3 S main * N.

2. The area of the circle lying at the base is expressed through its radius: S = П R².

So the volume of the first cone is V1 = П R1² H1.

According to the condition of the problem, the radius for the second was doubled, and the height was reduced by 3 times.

The formula for the volume is now: V2 = P (2 * R1) ² H1 / 3.

Let’s compare the first volume with the second

V2: V1 = P * 4 R1² H1 / 3: P R1² H1 = 4/3.

This means that the volume of the second cone has increased by 1 1/3 times.

Answer: The volume has increased 1 1/3 times.



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