Question

the height of a cone is 14 cm and the area of its base is321 cm sq.find the volume.​

Answer 1

SOLUTION:-

Given:

Height of the cone is 14cm.

Area of its base= 321cm²

Since,

We know that base of right circular cone is circular.So,

area of base=area of circle= πr²

Find radius:

$\pi {r}^{2} = 321 {cm}^{2} \\ \\ = > \frac{22}{7} \times {r}^{2} = 321 \\ \\ = > {r}^{2} = \frac{321 \times 7}{22} \\ \\ = > {r}^{2} = 102.13 \\ \\ = > r = \sqrt{102} \\ = > r = 10.10cm$

Radius= 10.10cm

Now,

Find volume:

We know that volume of cone=1/3πr²h:

$= > \frac{1}{3} \times \pi \times 10.10 \times 10.10 \times 14 \\ \\ = > \frac{1}{3} \times \pi \times 1428.14 \\ \\ = > \frac{1}{3} \times \frac{22}{7} \times 1428.14 \\ \\ = > \frac{31419.08}{21} \\ \\ = > 1496.14 {cm}^{3}$

So,

Volume of the right circular cone required= 1496.14cm³.

Hope it helps ☺️