Question

find the capacity on letres of a bucket 2cmin diameter at the top, 16cm in diameter at the bottom and 20cm deep

Answer 1

To find the capacity of the bucket in liters, we can model the bucket as a frustum of a cone (a cone with the top part cut off). The formula for the volume \( V \) of a frustum is given by:

\[
V = \frac{1}{3} \pi h (r_1^2 + r_2^2 + r_1 r_2)
\]

where:
- \( h \) is the height of the frustum,
- \( r_1 \) is the radius of the top base,
- \( r_2 \) is the radius of the bottom base.

### Step 1: Convert dimensions to radius and height
- The diameter at the top is 12 cm, so the radius \( r_1 = \frac{12}{2} = 6 \) cm.
- The diameter at the bottom is 16 cm, so the radius \( r_2 = \frac{16}{2} = 8 \) cm.
- The height of the bucket \( h = 20 \) cm.

### Step 2: Plug values into the formula
Now we can substitute these values into the volume formula:

\[
V = \frac{1}{3} \pi (20) (6^2 + 8^2 + 6 \cdot 8)
\]

Calculating the squares and the product:

\[
6^2 = 36, \quad 8^2 = 64, \quad 6 \cdot 8 = 48
\]

Now, substitute these into the equation:

\[
V = \frac{1}{3} \pi (20) (36 + 64 + 48)
\]

Calculating inside the parentheses:

\[
36 + 64 + 48 = 148
\]

Now substitute this back into the volume equation:

\[
V = \frac{1}{3} \pi (20) (148)
\]

Calculating:

\[
V = \frac{1}{3} \cdot \pi \cdot 2960
\]

Calculate \( \frac{2960}{3} \):

\[
\frac{2960}{3} \approx 986.67 \, \text{cm}^3
\]

### Step 3: Convert cubic centimeters to liters
Since 1 liter = 1000 cm³, we convert the volume to liters:

\[
V \approx \frac{986.67}{1000} \approx 0.987 \, \text{liters}
\]

### Final Answer
The capacity of the bucket is approximately **0.987 liters**.