Q) A cone and a cylinder have the same base radius and height. If the volume of the cylinder is 300 cm ³, find the volume of the cone.

Ans: [Approach: Given that the radius and height are the same, we will find a relation of r and h from the cylinder’s volume formula, and substitute it in the cone’s volume formula, and calculate the cone’s volume]

Step 1: It is given that the cone and the cylinder have the same base radius and height

∴ Radius: r_cylinder = r_cone = R cm

and Height: h_cylinder = h_cone = H cm

Step 2: We know that the volume of a cylinder is given by: V_cylinder = π r ² h

Given that the volume of the cylinder is 300 cm³

∴ 300 = π R ² H

∴ π R ² H = 300 ………… (i)

Step 3: Next, we know that the volume of a cone is given by: V_cone = π r ² h

∴ V_cone = π R ² H …….. (ii)

Step 4: By substituting the value of π R ² H from equation (i) into equation (ii), we get:

∴ V_cone = (300)

∴ V_cone = 100 cm ³

Therefore, the volume of the cone is 100 cm ³.

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