A cylindrical tank with diameter 20in. is half filled with water. How much will the water level in the tank rise if you place a metallic ball with radius 4in. in the tank? Round answer to the nearest tenth.

Question

wolf1728 · Answer

Volume of Ball = 4/3 * PI * r^3
Volume = 4/3 * PI * 64
Volume = 268.0825731063 cubic inches

Volume of a cylinder =   π • r² • height
A disk 1 inch thick (imagine a very flat cylinder) and a radius of 10inches
has a volume of
PI * r² * 1 
314.159265 cubic inches

This disk of 1 inch thickness and a volume of 314.159265 cubic inches would raise the water level exactly 1 inch.

So a ball of volume of 268.0826 cubic inches would raise the water level by 
(268.0826 / 314.1593) inches = 0.8533333248 inches or rounded to the nearest tenth = 0.9 inches

anonymous · Answer

Refer to a Mathematica solution attached.

wolf1728 · Answer

It's nice to know I got it right !!