Question
Download Solution PDF24 equal solid hemispheres are melted to form a right circular cylinder of radius 12 cm and height 24 cm. Find the radius of each solid hemisphere.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number of solid hemispheres = 24
Radius of the cylinder = 12 cm
Height of the cylinder = 24 cm
Formula used:
The volume of a hemisphere = (2/3)πr³
Calculation:
The total volume of the 24 solid hemispheres is equal to the volume of the cylinder.
Let's calculate the volume of the cylinder first using the formula:
The volume of the cylinder = πr²h
π(12 cm)² × 24 cm
144 × 24π
Since the 24 solid hemispheres have the same volume as the cylinder, the volume of each hemisphere can be calculated as:
Now, equate the volume of 24 hemispheres to the cylinder.
24 × (2/3) πr³ = 144 × 24π
(2/3)r³ = 144
r3 = 216
r = 6
Therefore, the radius of each solid hemisphere is 6 cm.
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