QuestionJune 4, 2025

Practice Problem #2 Water has density of 1000kg/m^3 .What is the weight of water displaced by a beach ball with a radius of 1.1 m if 85% of the ball is submerged?

Practice Problem #2 Water has density of 1000kg/m^3 .What is the weight of water displaced by a beach ball with a radius of 1.1 m if 85% of the ball is submerged?
Practice Problem #2
Water has density of 1000kg/m^3 .What
is the weight of water displaced by a
beach ball with a radius of 1.1 m if 85%  of
the ball is submerged?

Solution
4.6(248 votes)

Answer

The weight of the displaced water is approximately 4765.8 \, \text{N}. Explanation 1. Calculate the Volume of the Sphere Use the formula for the volume of a sphere: V = \frac{4}{3} \pi r^3. Here, r = 1.1 m. So, V = \frac{4}{3} \pi (1.1)^3. 2. Calculate Submerged Volume Since 85\% of the ball is submerged, multiply the total volume by 0.85: V_{\text{sub}} = 0.85 \times V. 3. Calculate Weight of Displaced Water Use the formula for weight: W = \rho \cdot V_{\text{sub}} \cdot g, where \rho = 1000 \, \text{kg/m}^3 and g = 9.81 \, \text{m/s}^2.

Explanation

1. Calculate the Volume of the Sphere<br /> Use the formula for the volume of a sphere: $V = \frac{4}{3} \pi r^3$. Here, $r = 1.1$ m. So, $V = \frac{4}{3} \pi (1.1)^3$.<br /><br />2. Calculate Submerged Volume<br /> Since $85\%$ of the ball is submerged, multiply the total volume by $0.85$: $V_{\text{sub}} = 0.85 \times V$.<br /><br />3. Calculate Weight of Displaced Water<br /> Use the formula for weight: $W = \rho \cdot V_{\text{sub}} \cdot g$, where $\rho = 1000 \, \text{kg/m}^3$ and $g = 9.81 \, \text{m/s}^2$.
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