To find the volume of a cylinder, we use the formula:
$$V = \pi \times r^2 \times h$$
Where:
* $V$ is the Volume
* $\pi$ (pi) is approximately $3.14159$
* $r$ is the radius (the distance from the center to the edge)
* $h$ is the height
The worksheet asks us to round all answers to the nearest hundredth (two decimal places). Note: Although the units on the sheet say "squared" ($cm^2$, $m^2$), volume is always measured in "cubed" units ($cm^3$, $m^3$). I will provide the numerical answers requested.
Here are the step-by-step calculations for each problem:
1. Top Left Cylinder
* Radius ($r$) = $8 \text{ cm}$
* Height ($h$) = $12 \text{ cm}$
* Calculation: $V = \pi \times 8^2 \times 12$
* $V = \pi \times 64 \times 12$
* $V = \pi \times 768 \approx 2412.743...$
*
Answer: $2412.74$
2. Top Right Cylinder
* Radius ($r$) = $5 \text{ m}$
* Height ($h$) = $3 \text{ m}$
* Calculation: $V = \pi \times 5^2 \times 3$
* $V = \pi \times 25 \times 3$
* $V = \pi \times 75 \approx 235.619...$
*
Answer: $235.62$
3. Middle Left Cylinder
* Radius ($r$) = $31 \text{ mm}$
* Height ($h$) = $77 \text{ mm}$
* Calculation: $V = \pi \times 31^2 \times 77$
* $V = \pi \times 961 \times 77$
* $V = \pi \times 73997 \approx 232467.546...$
*
Answer: $232467.55$
4. Middle Right Cylinder
* Radius ($r$) = $14 \text{ cm}$
* Height ($h$) = $9 \text{ cm}$
* Calculation: $V = \pi \times 14^2 \times 9$
* $V = \pi \times 196 \times 9$
* $V = \pi \times 1764 \approx 5541.769...$
*
Answer: $5541.77$
5. Bottom Left Cylinder
* Radius ($r$) = $2 \text{ cm}$
* Height ($h$) = $6 \text{ cm}$
* Calculation: $V = \pi \times 2^2 \times 6$
* $V = \pi \times 4 \times 6$
* $V = \pi \times 24 \approx 75.398...$
*
Answer: $75.40$
6. Bottom Right Cylinder
* Radius ($r$) = $9 \text{ m}$
* Height ($h$) = $6 \text{ m}$
* Calculation: $V = \pi \times 9^2 \times 6$
* $V = \pi \times 81 \times 6$
* $V = \pi \times 486 \approx 1526.814...$
*
Answer: $1526.81$
Final Answer:
Top Left: 2412.74
Top Right: 235.62
Middle Left: 232467.55
Middle Right: 5541.77
Bottom Left: 75.40
Bottom Right: 1526.81
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder worksheet answers.
