Question

The volume of water that a submerged object displaces is equal to the volume of the object. Find the radius of the sphere. Round your answer to the nearest tenth. $(1\mathrm{mL}=1{\mathrm{cm}}^3)$

Answer 1

Step 1: Calculate the volume displaced.

Volume of water before submerging the ball = $10$ mL

Volume of water after submerging the ball = $15$ mL

Volume of water displaced = $15-10=5$ mL

Since , $1\mathrm{mL}=1{\mathrm{cm}}^3$

Volume of water displaced = $5{\mathrm{cm}}^3$

Step 2: Calculate the radius of sphere

Volume of spherical ball:

$$\begin{gathered} =V=\frac{4}{3}{\mathrm{\pi r}}^3 \\ 5=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \frac{15}{4\mathrm{\pi }}={\mathrm{r}}^3 \end{gathered}$$

$$\begin{gathered} 1.19=r^3 \\ r=\sqrt[3]{1.19}(Takingcuberootnbothsides) \\ r=1.05 \end{gathered}$$

Hence the radius of the sphere is 1.05 cm.