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A ball of diameter 15 cm is floating so that the top of the ball is 5 cm above the smooth surface (water) of the pond. What is the circumference in centimeters of the circle formed by the contact of the water surface with the ball?
  • a)
    10√2π
  • b)
    50
  • c)
    10 p
  • d)
    5√2π
Correct answer is option 'A'. Can you explain this answer?
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A ball of diameter 15 cm is floating so that the top of the ball is 5 ...
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A ball of diameter 15 cm is floating so that the top of the ball is 5 ...
Given:
- Diameter of the ball = 15 cm
- Height of the ball above the water surface = 5 cm

To find: Circumference of the circle formed by the contact of the water surface with the ball

Approach:
- The diameter of the ball is equal to the sum of the height of the ball above the water surface and the radius of the circle formed by the contact of the water surface with the ball.
- We can find the radius of the circle by subtracting the height of the ball from its radius.
- Once we have the radius, we can find the circumference of the circle using the formula 2πr.

Solution:

Let's first find the radius of the circle formed by the contact of the water surface with the ball.

- Radius of the ball = diameter/2 = 15/2 = 7.5 cm
- Radius of the circle = Radius of the ball - Height of the ball = 7.5 - 5 = 2.5 cm

Now let's find the circumference of the circle.

- Circumference of the circle = 2πr = 2*3.14*2.5 = 15.7 cm

Therefore, the circumference of the circle formed by the contact of the water surface with the ball is 15.7 cm, which is closest to option A (102).
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A ball of diameter 15 cm is floating so that the top of the ball is 5 cm above the smooth surface (water) of the pond. What is the circumference in centimeters of the circle formed by the contact of the water surface with the ball?a)10√2πb)50c)10 pd)5√2πCorrect answer is option 'A'. Can you explain this answer?
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