Question 4 · Conical grain silo
Find the base area and the radius of a cone from its volume.
Maximum score · 1 pointsOn a farm they have installed a conical grain silo. We know the silo is $6$ metres high and has a capacity of $300\ \text{m}^3$. What area does its base cover? What is its radius?
Step-by-step solution
Volume of a cone: $V = \dfrac{1}{3} A_B \cdot h$. Substitute and solve for the base area:
$$300 = \dfrac{A_B \cdot 6}{3} \;\Longrightarrow\; A_B = 150 \text{ m}^2$$
The base is a circle, $A_B = \pi r^2$:
$$150 = \pi r^2 \;\Longrightarrow\; r = \sqrt{\dfrac{150}{\pi}} \approx 6{,}91 \text{ m}$$
Result: The base covers $150\ \text{m}^2$ and its radius is $\approx 6.91$ m.