The sum of the volume of two solid spheres is 1144/3 cm3. If the sum of their radii is 7 cm, then what will be the difference of the radii?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1 cm.
| Understanding/Application |
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Let radii of two spheres be r1 and r2 cm respectively. r1 + r2 = 7 ....(1 Sum of volumes of two sphere = 4π(r1)3/3 + 4π(r2)3/3 = 1144/3 88[(r1)3 + (r2)3]/21 = 1144/3 (r1)3 + (r2)3 = 91 ...(2 Cubing eq(1 on both side - (r1)3 + (r2)3 + 3(r1)(r2)(r1 + r2) = 343 Substituting values from eq(1 and (2, we get - 21r1r2 = 343 - 91 = 252 r1r2 = 12 ....(3 |
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Squaring eq(1 on both side, we get - (r1)2 + (r2)2 + 2r1r2 = 49 (r1 - r2)2 + 4 r1r2 = 49 Substituting value from eq(3 - (r1 - r2)2 + 48 = 49 (r1 - r2)2 = 1 r1 - r2 = 1 |