Question

Since the area of the circle is I the area of the square, the

Answer 1

Answer:

(b)

$V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]$ or $V_2 = \frac{1}{3}\pi r^2h$

Step-by-step explanation:

Given

$Ratio = \frac{\pi}{4}$

See attachment for complete question

Required

Determine the volume of the cone

The volume of a square pyramid is:

$V = \frac{a^2h}{3}$

Where

a = base dimension

From the attachment, the base dimension of the square pyramid is 2r.

So:

$a = 2r$

The volume becomes;

$V = \frac{(2r)^2h}{3}$

To calculate the volume of the cone, we simply multiply the given ratio and the volume of the prism.

So, we have:

$V_2 = Ratio * V$

$V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]$

$V_2 = \frac{\pi}{4} * \frac{(2r)^2h}{3}$

Open bracket;

$V_2 = \frac{\pi}{4} * \frac{4r^2h}{3}$

Cancel out 4

$V_2 = \pi * \frac{r^2h}{3}$

The above can be written as:

$V_2 = \frac{1}{3} * \pi r^2h$

$V_2 = \frac{1}{3}\pi r^2h$

So, we have:

$V_2 = \frac{\pi}{4} [ \frac{(2r)^2h}{3}]$

or

$V_2 = \frac{1}{3}\pi r^2h$