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प्रश्न
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
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उत्तर
Volume of first sphere = 27 × volume of second sphere
Let radius of first sphere = r1
And radius of second sphere = r2
Therefore, volume of first sphere = `4/3pir_1^3`
And volume of second sphere = `4/3pir_2^3`
i. Now, according to the question
= `4/3pir_1^3`
= `27 xx 4/3pir_2^3`
`r_1^3 = 27r_2^3 = (3r_2)^3`
`=>` r1 = 3r2
`=> r_1/r_2 = 3/1`
∴ r1 : r2 = 3 : 1
ii. Surface area of first sphere = `4pir_1^2`
And surface area of second sphere = `4pir_2^2`
Ratio in surface area = `(4pir_1^2)/(4pir_2^2)`
= `r_1^2/r_2^2`
= `3^2/1^2`
= `9/1`
= 9 : 1
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