Question

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

Answer 1

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:

$V=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\pi \times 4^3\\\\\approx 268.08\ cm^3$

#The volume of the water in the glass:

$V=\pi r^2 h\\\\=\pi \times 4^2\times 10\\\\\approx 50.27\ cm^2$

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

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

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).