Answer:
No. The new height of the water is less than the height of the glass(6.33 cm<10 cm)
Step-by-step 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:
[tex]V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3[/tex]
#The volume of the water in the glass:
[tex]V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2[/tex]
We then equate the two volumes to the glass' volume to determine the new height of the water:
[tex]V=\pi r^2h\\\\(206.08+50.27)=\pi r^2 h\\\\h=318.35/(\pi \times 4^2)\\\\=6.33\ cm[/tex]
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).
