Question 81

If the radius of a sphere is increased by 2 m, its surface-area is increased by 704 m$$^2$$. What is the radius of the original sphere?(Use $$\pi = \frac{22}{7}$$)

Solution

We know that surface area of a sphere = $$ 4 \pi r ^2 $$

According to the question,

$$ 4 \pi (r + 2)^2 - 4 \pi r^2 = 704 $$

$$ (r + 2)^2 - r^2 = \frac{704}{4 \pi} $$

$$ r^2 + 4r + 4 - r^2 = \frac{704}{4 \pi} $$

Use value of $$ \pi = \frac{22}{7} $$

On solving r = 13

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