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 226 cm³ 301 cm³ 452 cm³ 678 cm³

Explanation:

Step1: Find volume of one conical pot

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$. Given $r = 3$ cm and $h=8$ cm. Substitute values: $V_1=\frac{1}{3}\times\pi\times3^{2}\times8$.
$V_1=\frac{1}{3}\times\pi\times9\times8 = 24\pi$ cm³.

Step2: Find volume of 6 conical pots

Multiply the volume of one pot by 6. $V = 6\times V_1=6\times24\pi=144\pi$ cm³.
Approximate $\pi\approx3.14$. Then $V\approx144\times3.14 = 452.16$ cm³.
Rounding to the nearest cubic - centimeter, $V\approx452$ cm³.

Answer:

C. $452$ cm³