Question
Download Solution PDFThe material of a solid right circular cylinder is converted into the shape of a solid cone of equal radius. If the height of the cylinder is 8.8 cm, then the height of the cone is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Height of the cylinder = 8.8 cm
Concept:
We need to find the height of the cone formed when the material of the cylinder is converted.
Solution:
Since the volume of the material remains the same, we can equate the volumes of the cylinder and cone.
Volume of the cylinder = Volume of the cone
⇒ π × r2 × h_cylinder = (1/3) × π × r2 × h_cone
Canceling out the common terms:
⇒ h_cylinder = (1/3) × h_cone
Given that the height of the cylinder is 8.8 cm, we can find the height of the cone:
⇒ h_cone = 3 × h_cylinder = 3 × 8.8 cm = 26.4 cm
Therefore, the height of the cone is 26.4 cm.
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