Question

Find the exact volume of a cone 6yd height 5yd base

Answer 1

Answer:

The exact volume of a cone is 10 yd³.

Step-by-step explanation:

Given:

Height of cone (h) is 6 yd and base (b) is 5 yd.

Now, to get the volume we need to find the radius.

So, to find radius we put the formula of base:

Let the radius be $r$

Base=$\pi r^2$

$b=\pi\times r^{2}$

$5=\pi\times r^{2}$

Dividing both sides by π and using square root on both the sides:

$5\div \pi=(\pi \times r^{2}) \div \pi$

$\frac{5}{\pi}=r^{2}$

$\frac{5}{\pi}=r^{2}$

$r^{2}=\frac{5}{\pi}-----1$

Now, putting the formula for getting the volume (v) of cone:

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

$v=\pi\times r^{2}\times \frac{6}{3}$

$v=\pi\times r^{2}\times 2$

Substituting the value of $r^2$ from equation (1), we get:

$v=\pi\times \frac{5}{\pi}\times 2$

$v=10$ yd³

Volume of cone is 10 yd³

Therefore, the exact volume of a cone is 10 yd³.