Mathematics: Since the area of the circle is I the area of the square, the volume of the cone equals o I the volume of the pyramid or (ench or srh. o the volume of the pyramid or (2n o the volume of the pyramid or (2nm or s?h. o the volume of the pyramid or : ( 20%(h) or şir?h.

Ur name spell backward is anala...

Since the area of the circle is I the area of the

DestinyK8033

10.06.2021

(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:

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

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

0,0(0 оценок)