Q.If the radius of a sphere is increased by 2 cm, its curved surface area increases by 352 square centimeters. What was the original radius of the sphere? (a) 5 cm (b) 6 cm (c) 7 cm (d) 5.6 cm
Answer: B
Let the radius of the sphere be \( r \) cm. If increased by 2 cm, the new radius becomes \( r + 2 \) cm. Then, \[ 4\pi(r+2)^2 - 4\pi r^2 = 352 \] i.e., \[ 4\pi[r^2 + 4r + 4 - r^2] = 352 \] i.e., \[ \frac{4 \times 22}{7} [4r + 4] = 352 \] i.e., \[ 4r + 4 = \frac{352 \times 7}{88} \] i.e., \[ 4r = 28 - 4 \] i.e., \[ r = 6 \] ∴ The original radius of the sphere was 6 cm.
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