Volume of cones practice worksheet with problems and diagrams.

Here are the step-by-step solutions for each problem on the worksheet.

Formula Reminder:
The volume of a cone is calculated using the formula:
$$V = \frac{1}{3} \times \pi \times r^2 \times h$$
Where:
* $r$ is the radius (distance from the center to the edge).
* $h$ is the height.
* $\pi$ is approximately $3.14$.

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Part A: Find the volume of each cone

1) Radius ($r$) = 7 in, Height ($h$) = 9 in
* Step 1: Square the radius. $7 \times 7 = 49$.
* Step 2: Multiply by height and $\pi$. $49 \times 9 \times 3.14 = 1384.74$.
* Step 3: Divide by 3. $1384.74 / 3 = 461.58$.
* Volume = 461.58 in³

2) Diameter = 10 cm, Height ($h$) = 12 cm
* *Note: The image shows the full width (diameter) is 10, so we must find the radius first.*
* Step 1: Find radius. $10 / 2 = 5$ cm.
* Step 2: Square the radius. $5 \times 5 = 25$.
* Step 3: Multiply by height and $\pi$. $25 \times 12 \times 3.14 = 942$.
* Step 4: Divide by 3. $942 / 3 = 314$.
* Volume = 314.00 cm³

3) Radius ($r$) = 4 ft, Height ($h$) = 9 ft
* Step 1: Square the radius. $4 \times 4 = 16$.
* Step 2: Multiply by height and $\pi$. $16 \times 9 \times 3.14 = 452.16$.
* Step 3: Divide by 3. $452.16 / 3 = 150.72$.
* Volume = 150.72 ft³

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Part B: Find the volume from given parameters

4) Height = 10 in, radius = 12 in
* Step 1: Square the radius. $12 \times 12 = 144$.
* Step 2: Multiply by height and $\pi$. $144 \times 10 \times 3.14 = 4521.6$.
* Step 3: Divide by 3. $4521.6 / 3 = 1507.2$.
* Volume = 1507.20 in³

5) Radius = 2 ft, height = 5 ft
* Step 1: Square the radius. $2 \times 2 = 4$.
* Step 2: Multiply by height and $\pi$. $4 \times 5 \times 3.14 = 62.8$.
* Step 3: Divide by 3. $62.8 / 3 = 20.933...$
* Volume = 20.93 ft³

6) Radius = 8 yd, height = 13 yd
* Step 1: Square the radius. $8 \times 8 = 64$.
* Step 2: Multiply by height and $\pi$. $64 \times 13 \times 3.14 = 2612.48$.
* Step 3: Divide by 3. $2612.48 / 3 = 870.826...$
* Volume = 870.83 yd³

7) Height = 17 in, radius = 21 in
* Step 1: Square the radius. $21 \times 21 = 441$.
* Step 2: Multiply by height and $\pi$. $441 \times 17 \times 3.14 = 23547.78$.
* Step 3: Divide by 3. $23547.78 / 3 = 7849.26$.
* Volume = 7849.26 in³

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Part C: Word Problem

8) Santa hat with height 8 inches and radius 3 inches.
* Step 1: Square the radius. $3 \times 3 = 9$.
* Step 2: Multiply by height and $\pi$. $9 \times 8 \times 3.14 = 226.08$.
* Step 3: Divide by 3. $226.08 / 3 = 75.36$.
* Volume = 75.36 in³

Final Answer:
A)
1) 461.58 in³
2) 314.00 cm³
3) 150.72 ft³

B)
4) 1507.20 in³
5) 20.93 ft³
6) 870.83 yd³
7) 7849.26 in³

C)
8) 75.36 in³