Question

15. A cylindrical glass 10 cm tall and 8 cm in diameter is filled to 1 cm

from the top with water. If a golf ball 4 cm in diameter is placed into
the glass, will the water overflow?

Answer 1

No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)

Explanation:

-For the water in the glass to overflow, the volume of the inserted solid must be greater than the volume of the empty space or the ensuing height of water >height of glass.

#Volume of the golf ball:

`V=(4)/(3)\pi r^3\\\\=(4)/(3)\pi * 4^3\\\\\approx 268.08\ cm^3`

#The volume of the water in the glass:

`V=\pi r^2 h\\\\=\pi * 4^2* 10\\\\\approx 50.27\ cm^2`

We then equate the two volumes to the glass' volume to determine the new height of the water:

`V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi * 4^2)\\\\=6.33\ cm`

Hence, the glass will not overflow since the new height of the water is less than the height of the glass(6.33 cm<10cm).