The volumes of spheres A and B are in the ratio 125 : 64. If the sum of radii of A and B is 36 cm, then the surface area (in cm2) of A is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 1600 π
| Understanding | Application |
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The volume of spheres is directly proportional to the radii of the spheres. Surface Area of sphere = 4πr2 |
⇒ V1 / V2 = r13 / r23 ⇒ 125 / 64 = r13 / r23 ⇒ r1 / r2 = 5 / 4 Let r1 be 5k and r2 be 4k. ⇒ 4k + 5k = 36 ⇒ 9k =36 ⇒ k = 4 ⇒ r1 = 4 × 5 ⇒ 20 cm ⇒ S = 4π(20)2 ⇒ 1600π cm2 |