Question

a gardener uses a tray of 6 conical pots to plant seeds. each conical pot has a radius of 3 centimeters and a depth of 8 centimeters. about how many cubic centimeters of soil are needed to plant the full tray? round to the nearest cubic centimeter. \\(\bigcirc\\) \\(226\\,\text{cm}^3\\) \\(\bigcirc\\) \\(301\\,\text{cm}^3\\) \\(\bigcirc\\) \\(452\\,\text{cm}^3\\) \\(\bigcirc\\) \\(678\\,\text{cm}^3\\)

Explanation:

Step1: Recall cone volume formula

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$

Step2: Calculate volume of 1 pot

Substitute $r=3$, $h=8$:
$\frac{1}{3} \times \pi \times 3^2 \times 8 = \frac{1}{3} \times \pi \times 9 \times 8 = 24\pi \approx 75.398$ cm³

Step3: Find total volume for 6 pots

Multiply single pot volume by 6:
$6 \times 75.398 \approx 452.39$ cm³

Step4: Round to nearest whole number

$452.39 \approx 452$ cm³

Answer:

452 cm³ (Option C: $452 \text{ cm}^3$)