Problem Explanation:
The task involves using the water displacement method to determine the volume of various objects. The principle is simple: when an object is submerged in water, it displaces a volume of water equal to its own volume. This displaced volume can be measured by noting the change in water level in a graduated cylinder.
The formula to calculate the volume of the object is:
\[
V_{\text{object}} = V_f - V_i
\]
where:
- \( V_f \) is the final volume (water level after submerging the object),
- \( V_i \) is the initial volume (water level before submerging the object).
Step-by-Step Solution:
####
Top Row:
1.
Dinosaur:
- Initial Volume (\( V_i \)): 40 mL
- Final Volume (\( V_f \)): 50 mL
- Object's Volume: \( V_f - V_i = 50 \, \text{mL} - 40 \, \text{mL} = 10 \, \text{cm}^3 \)
2.
Swimmer:
- Initial Volume (\( V_i \)): 30 mL
- Final Volume (\( V_f \)): 40 mL
- Object's Volume: \( V_f - V_i = 40 \, \text{mL} - 30 \, \text{mL} = 10 \, \text{cm}^3 \)
3.
Fish:
- Initial Volume (\( V_i \)): 20 mL
- Final Volume (\( V_f \)): 30 mL
- Object's Volume: \( V_f - V_i = 30 \, \text{mL} - 20 \, \text{mL} = 10 \, \text{cm}^3 \)
####
Middle Row:
4.
Hammer:
- Initial Volume (\( V_i \)): 60 mL
- Final Volume (\( V_f \)): 70 mL
- Object's Volume: \( V_f - V_i = 70 \, \text{mL} - 60 \, \text{mL} = 10 \, \text{cm}^3 \)
5.
Hammer (different angle):
- Initial Volume (\( V_i \)): 50 mL
- Final Volume (\( V_f \)): 60 mL
- Object's Volume: \( V_f - V_i = 60 \, \text{mL} - 50 \, \text{mL} = 10 \, \text{cm}^3 \)
6.
Person:
- Initial Volume (\( V_i \)): 40 mL
- Final Volume (\( V_f \)): 50 mL
- Object's Volume: \( V_f - V_i = 50 \, \text{mL} - 40 \, \text{mL} = 10 \, \text{cm}^3 \)
####
Bottom Row:
7.
SpongeBob:
- Initial Volume (\( V_i \)): 30 mL
- Final Volume (\( V_f \)): 40 mL
- Object's Volume: \( V_f - V_i = 40 \, \text{mL} - 30 \, \text{mL} = 10 \, \text{cm}^3 \)
8.
SpongeBob with hat:
- Initial Volume (\( V_i \)): 20 mL
- Final Volume (\( V_f \)): 30 mL
- Object's Volume: \( V_f - V_i = 30 \, \text{mL} - 20 \, \text{mL} = 10 \, \text{cm}^3 \)
Final Answers:
\[
\boxed{
\begin{array}{ccc}
\text{Dinosaur} & \text{Swimmer} & \text{Fish} \\
10 \, \text{cm}^3 & 10 \, \text{cm}^3 & 10 \, \text{cm}^3 \\
\text{Hammer} & \text{Hammer (angle)} & \text{Person} \\
10 \, \text{cm}^3 & 10 \, \text{cm}^3 & 10 \, \text{cm}^3 \\
\text{SpongeBob} & \text{SpongeBob with hat} & \\
10 \, \text{cm}^3 & 10 \, \text{cm}^3 &
\end{array}
}
\]
Explanation:
In each case, the volume of the object is calculated by subtracting the initial water level from the final water level after the object is submerged. All objects displace 10 cm³ of water, indicating their volumes are all 10 cm³.
Parent Tip: Review the logic above to help your child master the concept of volume of irregular solids worksheet.
