A 30-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

Step-by-step explanation:

Length of:

First piece = x

Second piece = 4x

Third piece = 5x

Equation: 30 = 4x + 5x + x

Solving the Equation:

10x = 30  

x = 3

Lengths of:

First piece = 3 inches

Second piece = 12 inches

Third piece = 15 inches

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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