Question

The cone below has a base diameter of 20x cm. When the base of
The cone rests on horizontal ground it exerts a pressure of 650 N/m^2

a) Calculate the weight of the cone in terms of x and pie

Answer 1

Since the cone has a base diameter of 20x cm, the weight of the cone in terms of x and pie is 6.50πx² N

Pressure on the ground

The pressure on the horizontal ground due to the cone is given by P = W/A where

• W = weight of cone and
• A = area of base of cone

Weight of the cone

Making W subject of the formula, we have

W = PA

Since

• P = pressure = 650 N/m² and
• A = area of base of cone = πd²/4 where
• d = diameter of base of cone = 20x cm = 0.2x m

So, W = PA

W = Pπd²/4

W = Pπ(0.2x)²/4

W = 0.04Pπx²/4

W = 0.01Pπx²

Substituting the values of the variables into the equation, we have

W = 0.01Pπx²

W = 0.01 × 650 N/m² × π(x m)²

W = 6.50πx² N

So, since the cone has a base diameter of 20x cm, the weight of the cone in terms of x and pie is 6.50πx² N

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