Question

the radius of its base is 28 cm.
The height of a cone is 14 cm and the area of its base is 321 cm?. Find the volume.
​

Answer 1

Answer:

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:

\begin{gathered}\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\end{gathered}

πr

2

=321cm

2

=>

7

22

×r

2

=321

=>r

2

=

22

321×7

=>r

2

=102.13

=>r=

102

=>r=10.10cm

Radius= 10.10cm

Now,

Find volume:

We know that volume of cone=1/3πr²h:

\begin{gathered}= > \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}\end{gathered}

=>

3

1

×π×10.10×10.10×14

=>

3

1

×π×1428.14

=>

3

1

×

7

22

×1428.14

=>

21

31419.08

=>1496.14cm

3

So,

Volume of the right circular cone required= 1496.14cm³.