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Question
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is ______.
Options
4.2 cm
2.1 cm
2.4 cm
1.6 cm
Solution
A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is 2.1 cm.
Explanation:
The formula of volume of the cone is `1/3 pir^2 h`.
So, `1/3 pir^2 h = 1/3 pi (2.1)^2 xx 8.4`
Now, volume of sphere = `4/3 pir_1^3`
According to the question,
`4/3 pir_1^3 = 1/3 pi (2.1)^2 xx 8.4`
`4r_1^3 = (2.1)^2 xx 8.4`
`r_1^3 = ((2.1)^2 xx 8.4)/4`
`r_1^3 = (2.1)^2 xx 2.1`
`r_1^3 = (2.1)^3`
r1 = 2.1
Hence, the radius of the sphere is 2.1 cm.
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