Multiple choice

There is water to a height of $16cm$ in a cylindrical glass jar of radius $12.5cm$. Inside the water, there is a sphere of diameter $15cm$, completely immersed. By what height will water go down, when the sphere is removed?

  1. $\dfrac {10}{8}cm$
  2. $\dfrac {18}{5}cm$
  3. $\dfrac {10}{9}cm$
  4. $\dfrac {1}{9}cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the sphere is (4/3) * pi * r^3 = (4/3) * pi * (7.5)^3. The water level drop is equal to the volume of the sphere divided by the cross-sectional area of the jar (pi * 12.5^2). Calculation: (4/3 * pi * 7.5^3) / (pi * 12.5^2) = (4/3 * 421.875) / 156.25 = 562.5 / 156.25 = 3.6 cm, which is 18/5 cm.

AI explanation

When the sphere is removed, the volume of water that goes down equals the volume of the sphere, which is four by three pi r cubed. The radius of the sphere is fifteen divided by two, or seven point five centimeters, so its volume is four by three pi times seven point five cubed, equaling five hundred sixty two point five pi cubic centimeters. This volume equals the base area of the cylindrical jar times the drop in water height, giving pi times twelve point five squared times the height drop equals five hundred sixty two point five pi. Solving for the height drop gives five hundred sixty two point five divided by one hundred fifty six point two five, which equals eighteen by five centimeters.