john wants to know the volume of his gold ring in cubic centimeters. he gets a glass in the shape of a…

john wants to know the volume of his gold ring in cubic centimeters. he gets a glass in the shape of a rectangular prism with a base 3 cm by 2 cm and fills the glass with 3.1 cm of water. john drops his gold ring in the glass and measures the new height of the water to be 3.7 cm. what is the volume of johns ring in cubic centimeters? cm³

john wants to know the volume of his gold ring in cubic centimeters. he gets a glass in the shape of a rectangular prism with a base 3 cm by 2 cm and fills the glass with 3.1 cm of water. john drops his gold ring in the glass and measures the new height of the water to be 3.7 cm. what is the volume of johns ring in cubic centimeters? cm³

Answer

Explanation:

Step1: Find the base - area of the prism

The base of the rectangular prism is a rectangle with length $l = 3$ cm and width $w=2$ cm. The base - area $A$ of a rectangle is given by $A = l\times w$. So, $A=3\times2 = 6$ $cm^{2}$.

Step2: Find the change in water height

The initial height of water is $h_1 = 3.1$ cm and the final height of water after dropping the ring is $h_2 = 3.7$ cm. The change in height $\Delta h=h_2 - h_1$. So, $\Delta h=3.7 - 3.1=0.6$ cm.

Step3: Calculate the volume of the ring

The volume of the ring is equal to the volume of water displaced. The volume of water displaced $V$ is given by the product of the base - area of the prism and the change in water height, i.e., $V = A\times\Delta h$. Substituting $A = 6$ $cm^{2}$ and $\Delta h = 0.6$ cm, we get $V=6\times0.6 = 3.6$ $cm^{3}$.

Answer:

$3.6$